In his first remarks since his revolt, Prigozhin claims he wasn’t trying to overthrow Putin.

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.”

The Kremlin seeks to demonstrate business as usual after 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.

Global markets are muted after the short-lived mutiny in Russia.

How much a Russian ruble is worth

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 85 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 about half a 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 giving up most of their gains 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 rose more than 1 percent on Monday, extending recent gains because of drought in parts of the United States.

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

“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.

Major questions loom over the war after Wagner’s reversal.

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.

The E.U. pledges another $3.8 billion in potential military aid for 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.

Tracking Ukraine’s counteroffensive: Here’s the latest on the fighting.

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.

As the Dnipro River recedes after flooding, residents are returning home.

“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.

Did the Prigozhin revolt damage Putin’s ability to stay in 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.