“They wanted Russians to fight each other,” said Mr. Putin, Russia’s president. “They rubbed their hands, dreaming of taking revenge for their failures at the front and during the so-called counteroffensive.”

Throughout the day, the Kremlin had sought to project an air of normalcy, unity and stability, despite Mr. Putin’s absence from public view after perhaps the most serious crisis of his two-decade rule. When he finally emerged, the Russian leader skirted a host of unanswered questions left by the revolt. Instead, at the core of his five-minute speech on Monday was his insistence that he leads a nation and a government that present a united front to all threats.

“Civic solidarity has shown that any blackmail, attempts to create internal unrest, are doomed to failure,” he said.

The agreement that abruptly ended the mutiny on Saturday, with Wagner forces claiming that they had reached within 125 miles of Moscow, called for Mr. Prigozhin to go into exile in Belarus rather than face punishment, according to a Kremlin spokesman. Mr. Putin suggested that Wagner fighters who do not want to sign up with the regular Russian military may go there, too.

After his address, he was shown on television convening a meeting with his defense and interior ministers, prosecutor general, and chiefs of the security services and National Guard, to discuss how to respond to the episode.

Mr. Prighozhin, until recently a vital ally of Mr. Putin, said in an 11-minute, stream-of-consciousness voice memo posted on the messaging app Telegram on Monday that the government was trying to destroy Wagner, which he said would effectively have to disband by this coming Saturday.

“We went to demonstrate our protest, and not to overthrow the government in the country,” he said of the quixotic drive toward Moscow. But Kremlin officials have called it an act of treason, not protest.

In his audio message on Monday, Mr. Prigozhin renewed his sharp criticism of Russia’s military leaders for their handling of the invasion, and accused them again of attacking his fighters as they were preparing to give up their heavy weapons.

“The purpose of the campaign was to prevent the destruction of Wagner and to bring to justice those persons who, by their unprofessional actions, made a huge number of mistakes during this process,” he said.

It was not clear where Mr. Prigozhin was, or how he would be handled by a system that criminalizes mere dissent, much less armed rebellion. The Kremlin statement over the weekend that he would be allowed to go into exile was contradicted on Monday by reports in multiple state-controlled news outlets that he still faced investigation and a very real possibility of prosecution.

Nor was it clear what would happen to his tens of thousands of fighters, some of Russia’s most experienced and ruthlessly effective troops, or how that would affect the war in Ukraine. The government has required that all irregular forces fighting for Russia in Ukraine sign contracts with the Defense Ministry by July 1, spelling the end of Wagner’s semi-independence, but it is not clear how many have done so or will do so.

Mr. Putin indirectly addressed a question many people in Russia and abroad have been asking since the mutiny began: Why was it not crushed, swiftly and mercilessly, by Russia’s much larger military before Wagner could seize a regional military headquarters and push hundreds of miles toward Moscow?

“From the very beginning of the events, on my direct instructions, steps were taken to avoid a lot of bloodshed,” he said. “This took time, including to give those who made a mistake a chance to change their minds.”

Deputy Prime Minister Andrei Belousov said that the major M-4 highway — which was damaged over the weekend as Russian forces tried to slow the advance of Wagner troops toward Moscow — had been repaired and that all air and railway communications had been restored. Moscow’s mayor ended the restrictions that had been put in place as a result of the uprising and announced that school graduation ceremonies would take place this weekend.

Reinforcing the business-as-usual message, Russia released a soundless video of Defense Minister Sergei K. Shoigu on Monday, signaling that he remained in his post despite scathing criticism by Mr. Prigozhin over the conduct of the war.

At the White House on Monday, President Biden said he had convened a video meeting with allied leaders to discuss the mutiny, adding: “We made clear that we were not involved. We had nothing to do with it. This was part of a struggle within the Russian system.”

The administration has repeatedly signaled that it wanted Mr. Putin to, as Mr. Biden put it, have “no excuse to blame this on the West and to blame it on NATO,” which are supporting Ukraine with weapons, intelligence, training and finances.

On the battlefields of Ukraine, where Kyiv’s forces are mounting a counteroffensive to retake territory seized last year by Russia, there was no apparent change as a result of events within Russia, but some American officials and Western analysts said Russia’s military could suffer.

“Overall, Russian morale is likely to have been severely negatively affected by the turmoil,” said Aditya Pareek, an analyst at Janes, the defense intelligence firm.

But Franz-Stefan Gady, a consulting senior fellow at the International Institute for Strategic Studies, said it was too early to gauge the mutiny’s impact. On the front lines, Russian rates of fire have not decreased, he said, and no major Russian troop rotations have been observed.

For months, Mr. Prigozhin, a former prison inmate who parlayed political connections into a multi-armed business empire, has aimed a stream of stinging criticism at Russia’s military establishment, while claiming that Wagner deserved sole credit for some successes in Ukraine. He accused military leaders of undermining the war effort with incompetence and infighting, while withholding needed supplies from Wagner. With a base of support among pro-war Russians, he was widely seen as laying the groundwork for some kind of political career.

But early this month, the Defense Ministry issued the directive that irregular forces sign up with the military, and the order remained in place, despite Mr. Prigozhin’s bitter complaints and refusal to comply — an apparent signal that Mr. Putin had sided with Mr. Shoigu and the generals.

On Friday, Mr. Prigozhin accused the regular military of shelling Wagner troops, killing dozens of them — a claim that has not been independently corroborated — and his forces drove on Rostov-on-Don, a major city in southern Russia, where Wagner seized control of a hub for military operations in Ukraine.

The world watched in shock and fear as instability seemed to shake the nation with the world’s largest nuclear arsenal. Mr. Putin on Saturday vowed the harshest punishment for those who had “consciously chosen the path of betrayal.”

But then the Wagner forces halted, after Aleksandr G. Lukashenko, a Putin ally and president of Belarus, played intermediary. Wagner forces withdrew from Rostov-on-Don and the highway to Moscow, reportedly returning to their camps in Russian-occupied eastern Ukraine.

Valerie Hopkins reported from Berlin. Reporting was contributed by Andrés R. Martínez in Seoul, Eric Schmitt in Washington, Ivan Nechepurenko in Tbilisi, Georgia, and Daniel Victor and Gabriela Sá Pessoa in New York.

“It is very important to be here today,” Mr. Zelensky wrote in a message on Telegram, explaining his trip to the Donetsk region of eastern Ukraine.

In separate messages, Mr. Zelensky thanked soldiers for their defense of Ukraine, independence and freedom; called it an “honor to be with our heroes”; and posed for selfies with soldiers.

The statements came as the Kremlin sought to portray the Russian military as returning to normal after a weekend rebellion that shook President Vladimir V. Putin’s authority, in which mutinous mercenaries from the Wagner private military company, which has aided Russia’s war in Ukraine, got to within 125 miles of Moscow.

With questions still swirling on Monday about the ramifications of the armed uprising, and as Mr. Putin made his first public comments since the revolt was called off on Saturday to thank Russia’s military for fending off the rebellion, the office of Mr. Zelensky appeared keen on accentuating his relationship with Ukrainian troops.

Mr. Zelensky’s office posted a photo on Telegram during Mr. Putin’s brief televised address, showing Mr. Zelensky standing at a table with a commander.

It is unclear what effect the turmoil in Russia will have on the Ukrainian counteroffensive. So far, the situation on the front line has not changed significantly, though it remains possible that Ukraine may try to exploit any perceived Russian disarray.

Earlier on Monday, Ukrainian officials reported that Kyiv’s forces had recaptured the small village of Rivnopil in the country’s east, near a string of settlements they retook earlier this month.

“We are moving forward,” Gen. Oleksandr Syrsky, the commander of Ukraine’s land forces, said in a post on Telegram. But Ukrainian officials said that the fighting remained fierce and that Russia had increased its attacks in the east.

Mr. Zelensky acknowledged that the eastern front was “very difficult and hot” on Monday, according to his office, which said that he had told soldiers that “everyone in the country who is not at the front is well aware that you are doing the most difficult job today.”

Mr. Biden said he had instructed his national security team to brief him “hour by hour” and to “prepare for a range of scenarios.” He also said that he had convened a conference call to coordinate with some of the United States’ key allies as the mutiny led by the Wagner founder Yevgeny V. Prigozhin began unfolding over the weekend.

On the call, Mr. Biden said, the allies agreed to give Mr. Putin “no excuse to blame this on the West or to blame this on NATO.” He added, “We made clear that we were not involved. We had nothing to do with it.”

Mr. Biden said he and President Volodymyr Zelensky of Ukraine, whom he spoke with on Sunday, would stay in contact. Mr. Biden said that the United States would continue to assess the fallout from the crisis in Russia and closely align responses with its allies. Still, he cautioned, it was “still too early to reach a definitive conclusion about where this is going.”

Mr. Prigozhin was last seen in public late Saturday after calling off Wagner’s brief revolt. He agreed to call off his forces’ march to Moscow under a deal that would halt a criminal investigation into his activities and allow him to go to Belarus. On Monday, Mr. Prigozhin broke his silence to claim that his advance on Moscow had never been intended as a bid to seize power.

In a separate news briefing, the State Department spokesman, Matthew Miller, told reporters on Monday that he did not know whether Mr. Prigozhin was in Belarus and that he had “no assessment” of Mr. Prigozhin’s location at all. He added that the United States did not know what would happen to Wagner fighters in Ukraine or Africa, calling the situation “dynamic.”

Even so, Mr. Miller said, the significance of Mr. Prigozhin’s power play was clear.

“It is certainly a new thing to see President Putin’s leadership directly challenged,” he said, noting that Mr. Prigozhin had publicly questioned the rationale for Russia’s invasion of Ukraine, something that “we certainly have not seen coming from Russian officials previously.”

Mr. Miller added that the United States did “not take a position on the leadership of the Russian Federation. We do not take a position on the leadership of the Russian Ministry of Defense.”

“Our policies have always been with respect to actions that Russia has taken,” he said.

While Mr. Miller may have been articulating official U.S. policy, President Biden has previously expressed a different personal view.

“For God’s sake, this man cannot remain in power,” Mr. Biden said of Mr. Putin during a March 2022 visit to Poland.

Mr. Miller also said that the U.S. ambassador to Russia, Lynne M. Tracy, had contacted the Russian government on Saturday, reminding Russian officials of their obligations to protect the U.S. embassy and diplomatic personnel in Moscow.

Mr. Miller said that Ms. Tracy had also reiterated assurances that the Biden administration saw the uprising as an internal Russian matter, “one in which the United States is not involved and will not be involved.”

Mr. Putin opened Monday’s address with a forceful rebuke of the uprising. “Civic solidarity has shown that any blackmail attempts to create internal unrest are doomed to failure,” he said.

Though Mr. Prigozhin’s forces managed to take over the southern city of Rostov-on-Don and travel relatively unimpeded up a major highway toward the Russian capital, Mr. Putin sought to present a picture of Russian officials reacting in a timely and efficient manner to oppose the armed mutiny.

Executive and legislative power “at all levels” consolidated against the uprising, and along with public and religious organizations “took a firm unequivocal position in support of the constitutional order,” he said. “In fact,” he added, “the entire Russian society united and rallied everyone.”

In a deal brokered by President Aleksandr G. Lukashenko of Belarus, Mr. Prigozhin agreed to call off his revolt. Under the terms of that agreement, Mr. Prigozhin would be allowed to leave Russia for Belarus — and on Monday, Mr. Putin said that some of his Wagner fighters could do the same.

“The promise I made will be fulfilled,” Mr. Putin said, though he did not address Kremlin spokesman Dmitri S. Peskov’s assertion on Saturday that the security services would drop their investigation into Mr. Prigozhin. On Monday morning, several state-affiliated media outlets reported that the charges had not yet been dropped.

Mr. Peskov said that after the speech, which officials and state media outlets had billed as an important address but broke little new ground, Mr. Putin planned to meet with key Kremlin officials, including Defense Minister Sergei K. Shoigu. It seemed to be another sign of confidence and support for an official who had borne the brunt of Mr. Prigozhin’s ire.

Mr. Putin never uttered Mr. Prigozhin’s name, much as he avoided naming him during a fiery speech on Saturday that condemned the revolt. It is a tactic he has also used when speaking about the political dissident Aleksei A. Navalny.

But Mr. Putin made clear that he was referring to Mr. Prigozhin and the loyal group of Wagner fighters around him.

“They wanted Russians to fight each other,” Mr. Putin said. “They rubbed their hands, dreaming of taking revenge for their failures at the front and during the so-called counteroffensive. But they miscalculated,” he said, thanking the Russian military.

Some analysts said Mr. Putin’s speech offered little to the Russian public. Abbas Gallyamov, a former Kremlin speechwriter turned political consultant, said Mr. Putin’s speech was an “extremely weak performance” that only served to underscore Prigozhin’s strength.

A Kremlin spokesman, Dmitri S. Peskov, said Putin was holding a meeting Monday night with the heads of various Russian law enforcement agencies as well as the defense minister, Sergei K. Shoigu. Shoigu was a chief target of Prigozhin's criticism, both during his brief rebellion and long before it. Other attendees are the prosecutor general, interior minister, director of the Security Services, the head of the National Guard, and the head of the Kremlin administration, Peskov said.

Russian state media is reporting that part of Putin's meeting with his security chiefs will be televised. So we will hear from the Russian president again tonight.

Mr. Putin’s remarks appeared to be aimed at projecting unity and stability as questions swirled about the strength of his grip on power, which had rarely been questioned for more than two decades. He appeared on television a second time late Monday, in a brief snippet of a meeting with his defense and security chiefs, including Defense Minister Sergei K. Shoigu — a chief target of Mr. Prigozhin’s criticism before and during the revolt.

Mr. Putin spoke hours after Mr. Prigozhin made his first remarks since Saturday. The mercenary leader said that his rebellion was a protest against a new law that would require his fighters in Ukraine to sign contracts with the government by July 1. The goal, he claimed, had not been to seize power.

Both men had kept a low profile since Wagner’s audacious march toward Moscow ended on Saturday as part of a deal brokered by the president of Belarus. Under that agreement, Mr. Prigozhin agreed to turn his fighters around in return for his leaving Russia for Belarus.

Here’s what else to know:

• The future of the Wagner mercenary group remains unclear. Mr. Prigozhin said in his remarks earlier Monday that he had not been intending to oust Mr. Putin, and that he was only protesting the new law that he said would have effectively halted Wagner’s operations in Ukraine. His location remains unknown.

• As questions swirled on Monday about how the revolt’s fallout would affect the war and Mr. Putin’s future, the Kremlin sought to project an air of normalcy. Russia released a video of Mr. Shoigu for the first time since the uprising, appearing to signal that he remained in his post despite the scathing criticism from Mr. Prigozhin.

• While Mr. Putin’s address was being broadcast, the office of President Volodymyr Zelensky of Ukraine was underscoring his close ties to his own troops by releasing a photo of the president visiting soldiers near the front line in eastern Ukraine earlier Monday.

• President Biden said he had convened a conference call with some of the United States’ key allies as the mutiny began unfolding. On the call, Mr. Biden said, the allies agreed to give Mr. Putin “no excuse to blame this on the West or to blame this on NATO.” He added, “We made clear that we were not involved. We had nothing to do with it.”

• A Ukrainian counteroffensive is continuing, notching small gains and probing the Russian lines for vulnerabilities. Hanna Malyar, Ukraine’s deputy minister of defense, said on Monday that the Ukrainian military had recovered about 50 square miles along the southern front line since the counteroffensive began.

Wagner fighters who did not take part in the rebellion can sign contracts with the Defense Ministry and continue as fighters, the Kremlin said on Saturday, after Mr. Prigozhin said his forces were halting their advance on Moscow.

Andrei Kartapolov, a deputy of the Russian State Duma, the lower house of Parliament, said that lawmakers had been discussing legislation that would regulate mercenary groups such as Wagner. After its armed uprising, the fate of Wagner as an organization remains unresolved, he said.

“We need to ascertain its future,” he told Vedomosti, a Russian business daily, on Sunday. “Will they continue to exist? What will they be called? To whom will they report?”

He added: “We probably need to change their leadership. Appoint someone who would be more loyal, more definitive.”

Russian state media reported on Sunday that Wagner troops had returned to their camps in Ukraine’s eastern Luhansk region.

Following the Defense Ministry’s push to formalize such organizations within its hierarchy by forcing them to sign contracts, at least 10 volunteer groups have done so so far, according to Tass, a Russian state news agency.

As of now, private military companies operate in a legal gray area in Russia. The system benefits the Kremlin. For instance, it was able to deploy Wagner in covert or secretive operations in Ukraine and several African countries.

Wagner is the most potent and well-known group of the mercenary organizations in Russia.

Some of the other groups have existed under the auspices of the National Guard, including regiments led by Ramzan Kadyrov, the Chechen strongman, who backed President Vladimir V. Putin during the Wagner rebellion.

The Wagner group still has camps in the forests of Ukraine’s eastern Luhansk region. A video report from one of them last week, days before the uprising, shows a combination of dugout dormitories and tents, including amenities such as a sauna and laundry facilities. The report was made by Aleksandr Simonov, a military blogger known to be close to Mr. Prigozhin, but its authenticity could not be verified.

The fighters quoted in the video rejected reports that the group would be disbanded, with one saying, “We are waiting for out next task.”

Aleksandr G. Lukashenko, the autocratic president of Belarus and a reliable ally of Russia’s leader, Vladimir V. Putin, claimed to have brokered an end to the rebellion on Saturday. The details remain unclear, but the Kremlin said the deal allowed the Wagner leader to leave Russia for Belarus, alarming officials in Poland and Lithuania, which also borders Mr. Lukashenko’s country.

Although there was no indication that Mr. Prigozhin or any of his troops had arrived in Belarus, Poland’s prime minister and defense minister on Sunday visited troops stationed along the border, where they said security measures had been increased.

“As we have seen yesterday,” said the prime minister, Mateusz Morawiecki, “Lukashenko and Putin are capable of very bizarre actions.”

On the same day, Lithuanian officials said they were also diverting more intelligence capabilities to monitor the “political and security aspects of Belarus.”

“If Prigozhin or part of the Wagner group ends up in Belarus with unclear plans and unclear intentions, it will only mean that we need to further strengthen the security of our eastern borders,” Lithuanian President Gitanas Nauseda told reporters.

The turmoil in Russia has been a cause of concern — and titillation — in Eastern Europe. But analysts doubt that Mr. Prigozhin poses a threat to Poland or Lithuania, both NATO members. Instead, they wonder if the Poles and Lithuanians might be exploiting the disarray in Russia ahead of a major NATO summit in July — which will be held in Vilnius, Lithuania’s capital — to gain more weapons and support.

“The situation at the border is tense, of course, because Lukashenko is the Kremlin’s pawn,” said Nikita Grekowicz, an expert on Eastern Europe at the Helsinki Foundation for Human Rights in Warsaw.

But, he added, leaders in Poland — which is expected to hold parliamentary elections later this year — “are really addressing their voters” at home. Their posture is “an attempt at building an image of a strong Poland,” he said.

Polish and Lithuanian officials had already expressed concern about their borders with Belarus because of immigration issues. They have accused Mr. Lukashenko of encouraging migrants from Africa and the Middle East to pass through Belarus and travel onward to Poland and Lithuania, where local authorities have tried to turn them back.

Poland’s leaders have called this a deliberate strategy as part of “hybrid warfare,” and the country has already been steadily reinforcing its border with Belarus. Last year, it completed a towering, razor wire-topped wall separating the two countries, making it much harder for any migrants to enter.

OVERVIEW: For the past three weeks, the Ukrainian military has been waging a long-awaited counteroffensive to reclaim the thousands of square miles of territory that the Russian Army has seized in southern and eastern Ukraine. Bolstered by weapons and training from Western allies, Kyiv’s forces have notched small gains, breaking through a first line of Russian defenses and reclaiming several farming villages in the Donetsk and Zaporizhzhia regions. But Ukraine has also lost some of its newest tanks and armored vehicles and suffered an undisclosed number of casualties. The Ukrainian moves have been mostly small, focused attacks that are probing the Russian lines for vulnerabilities.

THE LATEST: Hanna Malyar, Ukraine’s deputy minister of defense, said on Monday that the Ukrainian military had recovered about 50 square miles along the southern front line since the counteroffensive began. In the east, she said, Ukrainian forces had recaptured the small village of Rivnopil, near a string of settlements it retook earlier this month. Military officials also said Ukrainian forces had pushed back Russian forces a mile or so in the area of Bakhmut, the ruined eastern city that Russia captured in May. The claims could not be independently verified.

“We are moving forward,” Gen. Oleksandr Syrsky, commander of Ukraine’s land forces, said in a post Monday on the Telegram app. But Ukrainian officials said that the fighting remained fierce and that Russia had increased its attacks in the east.

WHY IT MATTERS: Ukraine continues to claim small gains, but the world is watching to see what effect the turmoil in Russia following the short-lived mutiny by the Wagner mercenary leader will have on the counteroffensive. So far, the situation on the front line hasn’t really changed. Ukraine may try to exploit Russian disarray, but the rebellion over the weekend did not cause any Russian ground units to leave their positions in southern or eastern Ukraine, American officials said. And there did not seem to be any immediate defensive gaps in Russian lines to exploit, according to American officials and independent analysts.

Ukraine has created huge expectations, announcing for months that it would launch a decisive counteroffensive. So far, its gains have been limited. But military analysts say the campaign is still in its early stages and that Ukraine has yet to commit the full bulk of its forces.

Cassandra Vinograd contributed reporting.

Meeting in Luxembourg on Monday, Mr. Borrell and European foreign ministers described the rebellion led by Yevgeny V. Prigozhin, the chief of the Wagner mercenary group, as mainly a Russian domestic matter but noted that it demonstrated the importance of European nations’ remaining united on Ukraine.

“What has happened during this weekend shows that the war against Ukraine is cracking Russian power and affecting its political system,” Mr. Borrell said.

Catherine Colonna, the French foreign minister, told reporters before the meeting that although the Wagner mutiny showed “internal tensions” within the Russian political system, it was too early to draw definitive conclusions. “There are many uncertainties and we probably have not yet seen all the consequences of these events,” she said.

Moscow’s full-scale invasion of Ukraine, which began 16 months ago, has prompted the European Union to impose successive rounds of sanctions against Moscow and to sharply reduce imports of Russian oil and gas.

Aurelien Breeden contributed reporting.

Mr. Prigozhin said the protest was aimed at a move by the Ministry of Defense to force his mercenaries to sign contracts with the government, which he said would have effectively halted Wagner’s activities in Ukraine as of July 1. The fighters, Mr. Prigozhin said, were planning to give up their heavy weapons to the Russian Army until they were attacked from behind on Friday night, killing at least 30 Wagner soldiers — a claim for which there has been no independent evidence.

That’s when, he said, he decided to send one group of fighters to take the city of Rostov-on-Don, the home of the Russian southern command about 60 miles from the border with Ukraine, and another group to Moscow to register their anger.

“The purpose of the campaign was to prevent the destruction of the Wagner PMC and to bring to justice those persons who, by their unprofessional actions, made a huge number of mistakes during this process,” he said, obliquely referring to the Defense Ministry leadership.

The Wagner founder has spent months assailing Russia’s military leadership, which Mr. Prigozhin has long feuded with and accused of mismanaging the war effort. In Telegram posts that mixed self-aggrandizing statements and profanity-laced complaints, he accused military leaders of failing to supply his fighters with ammunition even as they were engaging in one of the bloodiest fights of the war, the taking of the ruined city of Bakhmut.

But Mr. Prigozhin had not been heard from since he called off his mutiny on Saturday, adding to the confusion surrounding an episode that had challenged Russia’s veneer of political stability. Hours after President Vladimir V. Putin of Russia labeled him a traitor and vowed to hold him accountable, Mr. Prigozhin ceased his advance on Moscow and agreed to withdraw from Rostov-on-Don under a deal that would drop the investigation of him and allow him to go to Belarus.

His voice memo, some analysts suggest, is a sign he wants to continue to be active in political and military affairs. In it, Mr. Prigozhin praised his fighters, saying they had shown professionalism and given the Russian public a “master class” in how the invasion of Ukraine should have been initiated last year. If Wagner had been in charge, he claimed, the completion of Russia’s military goals would have taken mere “days.”

Although the Kremlin said on Saturday that the deal to end hostilities — which Mr. Prigozhin again said he accepted in order to avoid bloodshed — would drop the case against him, there were signs on Monday that Mr. Prigozhin could still face charges.

According to Russian media reports published on Monday, the criminal case against Mr. Prigozhin remains open and the charges against him have not been dropped. Kommersant, a Russian newspaper, and the country’s three main news agencies — Tass, RIA and Interfax — all reported that the Federal Security Service, or F.S.B., continued to investigate.

The publications, all either state-controlled or affiliated with the Kremlin, cited anonymous sources, so their reports could not be independently verified. If the proceedings continue, Mr. Prigozhin could face up to 20 years in prison.

Even if the case is dropped, critics of Belarus’s president, Aleksandr G. Lukashenko, have raised doubts over whether Mr. Prigozhin would be safe there, given the government’s close ties to Mr. Putin, who has been a crucial source of support for Mr. Lukashenko.

Mr. Prigozhin was last seen in public late Saturday, smiling and shaking hands with supporters when he left the southern Russian city of Rostov-on-Don after he called an end to his brief uprising and turned back the column of soldiers he had sent on a march to Moscow.

Since then, his location has been unknown. On Sunday evening, Mr. Prigozhin’s press service told RTVI, a Russian TV channel, that he “says hi to everyone and will answer questions” when he has good cellphone reception.

Despite the severity of Mr. Prigozhin’s actions over the weekend, some Russian officials have been reluctant to criticize Wagner fighters, who have proven themselves to be effective, if brutal, in fighting on Russia’s behalf in Ukraine and in other conflicts.

Andrei Kartapolov, the chairman of the Russian Parliament’s defense committee, said Sunday that the Wagner fighters who took over the army headquarters in Rostov-on-Don “did not do anything reprehensible” and had simply “followed the orders of their command.”

“They didn’t offend anyone, they didn’t break anything,” he said. “No one has the slightest claim against them — neither the residents of Rostov, nor the military personnel of the Southern Military District, nor the law enforcement agencies.”

How much a Russian ruble is worth

Stock markets in the United States fell slightly and in Europe rose slightly, though investor attention had already begun pivoting to other things beyond Russia before the trading day’s end.

Trading in Russian assets, largely off-limits to international investors because of sanctions, showed the effects of the instability, but the moves were still relatively muted.

Although the mutiny by Yevgeny V. Prigozhin’s Wagner paramilitary group “occupied news headlines,” Paul Donovan, the chief economist at UBS Global Wealth Management, wrote in a morning research note, “financial markets have bordered on indifference.”

Russia’s main stock indexes fell more than 1 percent on Monday and the country’s currency traded its lowest value in more than a year, at around 84 rubles to the dollar. Some local banks had been quoting prices above 90 rubles over the weekend, suggesting that conditions had calmed somewhat.

The ruble remains more valuable than it was immediately after Russia’s full-scale invasion of Ukraine 16 months ago, although global trade in the currency has been hit severely by sanctions, muddying signals sent by the market. The ruble has recorded a steady slide over the past year, as oil prices have come down from the spike shortly after the invasion.

In choppy trading, oil prices rose slightly on Monday, extending late Friday’s gains, as Mr. Prigozhin’s rebellion initially took shape. Brent crude, the international benchmark, gained less than 1 percent, remaining within the range of trading seen over the past few months.

Russia is the world’s third-largest oil producer, after the United States and Saudi Arabia, and now exports much of its crude to China and India after embargoes sharply curtailed sales to Europe, once the key market for Russian oil.

Investors may place “a moderately higher probability that domestic volatility in Russia leads to supply disruptions or has a sizable negative impact on oil supply at some point in the future,” analysts at Goldman Sachs noted, but they added that it was too early to price in any long-term effects from the mutiny. Oil prices have been subdued by fears of a slowing global economy, despite efforts by major producers, including Saudi Arabia, to cut output to halt the slide.

Moves in natural gas markets were more pointed, with European benchmark prices jumping in early trading before retreating later in the day. Europe still imports some Russian gas by sea, though the flow of piped gas has been curtailed by sanctions and the sabotage of the Nord Stream pipeline.

Russia is also a major wheat producer. Global futures for the grain initially rose on Monday, extending recent gains because of drought in parts of the United States, before falling back.

Despite the lack of major market moves, some investors warned that the instability in Russia and increased unpredictability leave markets vulnerable.

“The immediate market impact of the weekend’s events is muted,” said Paul Christopher, head of global investment strategy at Wells Fargo Investment Institute. “But the war now has the potential to affect markets suddenly and more unpredictably than we’ve seen since the early days of the invasion.”

Stanley Reed contributed reporting.

The flooding unleashed by the dam’s destruction killed dozens of people, forced the evacuation of thousands more and aggravated a humanitarian crisis in a region on the front lines of the war. Kherson, which includes both Ukrainian- and Russian-controlled areas, was one of the regions most affected by the disaster.

“We are working to return normal life to the liberated Kherson region,” the environment ministry said, referring to the Ukrainian-held part of the region. Authorities were still working to clean cities, restore electricity and disinfect the water supply. Officials are also working to remove explosives found in flood-hit areas.

The Kakhovka Reservoir, which was drained when the dam was destroyed, is the largest body of freshwater in Ukraine, supplying small homes and large industries. It was also a main source of water used to cool the Zaporizhzhia Nuclear Power Plant’s reactors.

On June 6, the dam collapsed after an explosion. An investigation by The New York Times has shown that evidence suggests that Russia, which controlled the dam, was likely responsible for the blast.

American officials saw the episode as proof of Mr. Putin’s eroding strength. The chaos presented perhaps the strongest challenge to his iron-fisted authority in his decades of leading the country. Mr. Prigozhin publicly assailed Mr. Putin’s rationale for the war and was labeled a traitor. Hours later as his soldiers inched closer to Moscow, Mr. Prigozhin agreed to end his brief insurrection.

But as of Monday morning, Mr. Prigozhin’s whereabouts was unknown. The deal brokered to end his march toward Moscow allowed him to move to Belarus without facing charges in Russia, and made it unlikely he that he could continue to lead troops in Ukraine.

If Mr. Prigozhin abides by the agreement and moves to Belarus, he could potentially still face consequences. Russian special services have sometimes entered Belarus’ territory to capture its enemies.

The immediate impact on the front lines in Ukraine is even less clear. The mercenary force has played a crucial role in the campaign to control parts of eastern Ukraine, particularly the ruined city of Bakhmut. Part of the group will sign contracts with the Russian Ministry of Defense, but it is unclear if the men fighting in Ukraine will remain the aggressive fighting force it has been since the beginning of the invasion.

The uncertainty about the future of Wagner’s soldiers, especially those that are well-trained, could bring some relief for the Ukrainian forces. The Ukrainian military could capitalize on the disorder and low morale of the Russian in the fighting zones to make progress in its long-awaited effort to reclaim territory that Russia had seized.

Mr. Putin, too, is keeping a low profile. He has not been seen publicly since a five-minute speech on Saturday in which he declared Mr. Prigozhin a traitor and promised to quash the mutiny.

In the Kremlin’s telling, the Russian leader was hard at work, according to statements released by the government on Monday. Mr. Putin, the Kremlin said, had held several phone calls with allies including the emir of Qatar, Sheikh Tamim bin Hamad al-Thani, and President Ebrahim Raisi of Iran. Both leaders expressed support for the Russian leadership, according to the statements.

Russia released a video of Defense Minister Sergei K. Shoigu for the first time since the short-lived uprising, appearing to signal that he remained in his post despite scathing criticism by Mr. Prigozhin for the conduct of the war in Ukraine. The Russian Defense Ministry said Mr. Shoigu had traveled to a command post involved in the war, but did not specify when or where the visit occurred, and some Russian military bloggers said the video had been filmed before the uprising.

In a meeting with senior officials televised on Monday, Prime Minister Mikhail V. Mishustin acknowledged that “an attempt was made to destabilize the internal situation in Russia,” but insisted that members of the government continued working as usual. “Under the leadership of the president, they acted clearly, harmoniously, and maintained a stable situation at all levels,” Mr. Mishustin said.

The Russian authorities also sought to show that security had been restored. Deputy Prime Minister Andrei Belousov said that the major M-4 highway — which was damaged over the weekend as Russian forces tried to slow the advance of Wagner troops toward Moscow — had been repaired and that all air and railway communications had been restored. Moscow’s mayor on Monday morning also ended the restrictions that had been put in place in the city as a result of the uprising and announced that school graduation ceremonies would take place this weekend.

The rebellion led by Mr. Prigozhin, in which fighters from his Wagner private military company captured a key Russian military installation in the south and moved nearly halfway toward Moscow, has posed the biggest threat to Mr. Putin’s rule in more than two decades.

Mr. Prigozhin, once a close ally and confidant of Mr. Putin, had for months publicly criticized Mr. Shoigu and other military leaders, accusing them of mismanaging the war in Ukraine and starving his troops of ammunition. Russia’s military has relied on Wagner, a force with thousands of highly skilled troops, to engage Ukraine’s military in some of the bloodiest battles since Russia invaded in February 2022.

The rebellion, which barely lasted 24 hours, ended on Saturday, when the leader of Belarus, a close ally of Mr. Putin, offered Mr. Prigozhin exile in his country. Mr. Putin’s government said it had dropped the charges against Mr. Prigozhin and said the Wagner troops could enlist in the military and would not face discipline. But on Monday, several Russian news outlets controlled by or affiliated with the Kremlin reported that a criminal case against Mr. Prigozhin for his role in the uprising remained open.

In his absence, he left stunned Russians wondering how the leader of a paramilitary group, Yevgeny V. Prigozhin, could stage an armed mutiny on Saturday that threatened to reach Moscow. And it raised uncomfortable questions about the Russian president’s future: What did his failure to prevent the revolt mean for their security — and his staying power?

Russians with ties to the Kremlin expressed relief on Sunday that Mr. Prigozhin’s uprising did not spark a civil war. But at the same time, they agreed that Mr. Putin had come off looking weak in a way that could be lasting.

Konstantin Remchukov, a Moscow newspaper editor with Kremlin connections, said in a telephone interview that what once had seemed unthinkable was now possible: that people close to Mr. Putin could seek to persuade him not to stand for re-election in Russia’s presidential vote next spring.

The idea that “Putin is in power and provides stability and guarantees security — it suffered a fiasco on the 24th,” Mr. Remchukov said. “If I was sure a month ago that Putin would run unconditionally because it was his right, now I see that the elites can no longer feel unconditionally secure.”

“Stability” was the Kremlin’s refrain amid the 2020 referendum that cleared the way for Mr. Putin to serve two additional terms, until 2036. And for the elite, the sting of Western sanctions has been compensated by the new business opportunities of Russia’s wartime economy and a domestic market suddenly free of competition from many Western businesses.

But Mr. Prigozhin’s challenge to the Kremlin’s authority this weekend upended that calculus. Mr. Putin lost more than his reputation for providing stability: That Mr. Prigozhin and his forces were not punished punctured Mr. Putin’s reputation as a leader who would not tolerate disloyalty.

That impression was compounded by reports that Prigozhin forces had shot down Russian combat aircraft. In addition, Mr. Putin called Mr. Prigozhin a traitor after he launched his insurrection and questioned the rationale for the war in Ukraine.

Yet those transgressions melted away with the deal that ended the crisis, making Mr. Putin look less in control of the Russian state than previously known. And foreign adversaries were quick to seize on that theme.