Prigozhin says his forces have begun withdrawing from Bakhmut.

Ukraine has conceded that Russian forces control nearly the entire city and has said that its forces are shifting their focus to make it difficult for Russia to hold Bakhmut or move deeper into eastern Ukraine. On Thursday, a deputy Ukrainian defense minister, Hanna Maliar, said that Ukrainian troops controlled an area just southwest of Bakhmut and were trying to make further gains on the outskirts.

“In the Bakhmut direction, the enemy is trying to stop our advance on the flanks with artillery fire,” Ms. Maliar said. “Now the enemy is pulling up additional units to the flanks for reinforcement.”

Regular Russian Army units had replaced Wagner fighters in Bakhmut’s suburbs, Ms. Maliar added, while Wagner forces remained inside the city.

Mr. Prigozhin signaled that Wagner’s pullout would take several days, saying in a video statement published on the messaging app Telegram that all its troops would leave Bakhmut and head to training camps by Wednesday.

In an earlier statement this week, Mr. Prigozhin had said that, starting June 1, “not a single Wagner fighter will be at the forefront until we undergo re-formation, re-equipment and additional training.”

“We will get rest and get ready,” he said in the latest video. “And then we will receive a new task.”

In the video on Thursday, Mr. Prigozhin is shown visiting what he claims are Wagner positions in Bakhmut and telling his soldiers to hand over their positions to Russian troops.

“Leave them soap, but take away your toothbrushes,” he says. No Russian Army troops are seen in the roughly three-minute clip.

Mr. Prigozhin, a tycoon closely aligned with President Vladimir V. Putin, has been among the most vocal critics of Russian military leadership, accusing them of incompetence and corruption, although he has not criticized Mr. Putin.

He has apparently been emboldened by his mercenaries’ brutal effectiveness in Bakhmut, where ill-trained former prisoners mounted near-suicidal ground assaults against Ukrainian defenses. According to Mr. Prigozhin, 20,000 Wagner troops, half of whom were former convicts, died in Bakhmut, although a State Department spokesman said that was a significant undercount of Russia’s casualties in the battle. Ukraine, too, is believed to have suffered huge losses in the fighting.

Ukraine and Russia engage in dueling drone attacks.

Ukraine has spent weeks targeting key Russian command and control centers, rail lines, air fields and other military installations across occupied territories with the apparent aim of limiting Moscow’s ability to move troops and equipment quickly and effectively.

This month, President Volodymyr Zelensky said that Ukraine was “ready” to launch its long-anticipated counteroffensive but needed more time for Western weapons to arrive to prevent mass casualties. But Mykhailo Podolyak, a senior adviser to Mr. Zelensky, said on Thursday that recent military actions were all part of the Ukrainian counteroffensive, which he said would not be marked by a “single event.”

There are “dozens of different actions,” he said in a post on Twitter, to destroy the “occupation forces in different directions, which have already been taking place yesterday, are taking place today and will continue tomorrow.”

“Intensive destruction of enemy logistics is also a counteroffensive,” he added.

Ukrainian military actions are deliberately shrouded in confusion to try to keep the Russian forces off-balance. Military analysts have said that Kyiv will most likely use the fog of war, deliberate feints and active deception to help maintain an element of surprise for offensive actions that have been openly telegraphed for months.

But at some point, Ukrainian ground forces will need to break through Russian lines and infantry soldiers will have to reclaim land if Ukraine is to drive Russian forces out of vast swaths of occupied territory in the east and south.

Where, when, and how the Ukrainian military will try to do that remains a tightly guarded secret known to only a small group of senior leaders, Ukrainian officials have said.

Vadym Skibitsky, Ukraine’s deputy intelligence chief, said that disrupting Russian military movement in Crimea was essential to the Ukrainian campaign.

“Their reinforcements and the redeployment of troops, the supply of ammunition and equipment in the occupied territories all go through Crimea,” he told the German publication Welt in an interview published on Thursday.

Crimea holds enormous symbolic and military value for the government of President Vladimir V. Putin, who seized the peninsula in 2014 and has described it as a centerpiece of what he sees as Russia’s national restoration.

The Kremlin-installed governor of Crimea, Sergei Aksyonov, said on Thursday that multiple Ukrainian drone attacks had been thwarted across the territory.

The Russian-appointed governor of the Crimean port of Sevastopol, Mikhail Razvozhaev, said that two aerial drones had been shot down with small arms and that several maritime drones had been disabled using electronic warfare tools that jammed their signals.

The claims could not be independently verified.

At the same time, Russia also continued an aerial bombardment, including at least the 12th assault aimed at the capital, Kyiv, this month alone. Explosions echoed across the city through the night as drones were shot out of the sky during an attack that lasted some three hours.

“The enemy continues to use attack tactics in several waves, with intervals between groups of attacking drones,” the Kyiv regional military administration said in a statement. “This is how the Kremlin’s army is trying to achieve its goals, including exhausting our antiaircraft defense.”

Mykola Oleshchuk, commander of the Ukrainian Air Force, said that air defenses had shot down “36 out of 36” Iranian-made Russian attack drones.

Wagner’s withdrawal from Bakhmut would present a test for the Russian Army.

Mr. Prigozhin said Thursday that his fighters would “get rest and get ready,” before receiving “a new task” to perform in Ukraine. It is not clear how many Wagner troops remain in Bakhmut. American officials estimated in December that Wagner had about 50,000 fighters in Ukraine, including 10,000 experienced volunteers and 40,000 former prisoners who were granted pardons in exchange for military service.

For many supporters of Russia’s invasion of Ukraine, the Wagner group, with its harsh discipline and agile decision-making, has become a model for what the Russian Army, plagued by cumbersome bureaucracy, should look like.

Mr. Prigozhin has criticized Russia’s military leadership repeatedly. But Wagner and the Russian Army are also dependent on each other. While Mr. Prigozhin has some of the best assault troops fighting on the Russian side, the defense ministry holds vastly more weapons supplies, much to Mr. Prigozhin’s recent frustration.

In Ukraine, the Wagner group has sometimes served as an emergency force for Russia, engaging in battle when the situation appeared desperate. Weeks into the Russian invasion, Wagner troops helped capture the eastern town of Popasna, eventually allowing Russia to make further advances in the Donbas region. And Wagner’s grueling, bloody campaign in Bakhmut also allowed regular Russian forces to focus elsewhere, including on training additional troops and fortifying defenses.

Mr. Prigozhin signaled on Thursday that Wagner forces would rest and retrain after leaving Bakhmut, “and then we will receive a new task.”

Mr. Kuznets said that if Wagner troops are redeployed in Ukraine, they would likely be sent to areas surrounding Bakhmut or in southern Ukraine, an area that could be a focus of a Ukrainian counteroffensive.

While the Russian military leadership might prefer not to rely on Wagner for assistance again, he said, Moscow’s lack of sufficient troops makes Wagner’s eventual redeployment in Ukraine “inevitable.”

The Wagner group forecasts disaster if Russia does not move into total war footing.

He has been further empowered by his notorious mercenary force’s role in the recent conquest of Bakhmut, Russia’s first battlefield victory in months. However, Russian state media has kept his name out of its coverage of those events, showing how Russia’s propaganda machine has been hiding elite infighting and problems on the front line from the Russian people.

In the interview, Mr. Prigozhin called for total war — something Mr. Putin has carefully avoided, seeking to reassure his people that their lives will not be disrupted by the “special military operation” in Ukraine. That position has grown harder to maintain as the war drags on and Russian losses mount.

The Kremlin, Mr. Prigozhin said, must declare a new wave of mobilization to call up more fighters and declare martial law and force “everyone possible” into the country’s ammunition production efforts.

“We must stop building new roads and infrastructure facilities and work only for the war, to live for a few years in the image of North Korea,” he said. “If we win, we can build anything. We stabilize the front and then move on to some kind of active action.”

The alternative, he said, is more violence, but inside Russia, perpetrated by ordinary people fed up with elites, whom Mr. Prigozhin characterized as ignoring the reality of war but not doing enough to win it.

“The children of the elite smear themselves with creams, showing it on the internet, ordinary people’s children come in zinc, torn to pieces,” he said, referencing the coffins of dead soldiers, and adding that those killed in action had “tens of thousands” of relatives. “Society always demands justice, and if there is no justice, then revolutionary sentiments arise.”

Mr. Prigozhin said his Wagner force alone had lost 20,000 men during the war in Ukraine, half of whom had been recruited from prisons. Those convict fighters represent 20 percent of the total number of imprisoned convicts who joined the fighting force.

A State Department spokesman, Matthew Miller, said that the United States considered Mr. Prigozhin’s number a significant undercount of his losses. Even so, it is significantly higher than the Russian Armed Forces’ losses that the Kremlin has acknowledged. While American estimates range significantly higher, the Russian government has admitted only the deaths of 6,000 soldiers — statistics last publicly shared in September.

Mr. Prigozhin’s comments in the interview came after an incursion into Russia’s Belgorod region by Ukraine-aligned militants. The fighters, ethnic Russians who seek Ukraine’s victory, apparently used U.S.-made armored vehicles, and instigated the fiercest fighting on Russian soil since the war started 15 months ago.

Mr. Prigozhin said Ukraine had “one of the strongest armies in the world” and added that the violence at the border reflected poor leadership at the highest level of Russian military. He has often singled out Defense Minister Sergei K. Shoigu as the object of his ire, and in the interview, Mr. Prigozhin defined his personal credo as, “I love my motherland, I serve Putin, Shoigu should be judged and we will fight on.”

In brief remarks during a meeting with colleagues on Wednesday, Mr. Shoigu offered no reaction to Mr. Prigozhin’s comments and maintained that Russia would “respond promptly and extremely harshly” to any further incursions by “Ukrainian militants.”

Many analysts and other observers marvel at Mr. Prigozhin’s regular diatribes against Russia’s elite in a society that is strictly controlled, and especially his targeted criticisms of Mr. Shoigu.

“He is playing a very dangerous game,” one wealthy Moscow-based businessman said of Mr. Prigozhin in an interview with The New York Times in late March, asking for anonymity to discuss a prominent Kremlin-connected individual. “If he doesn’t stop, he will wind up like Aleksei Navalny.” Mr. Navalny, Russia’s most prominent opposition politician, is now in poor health in a penal colony.

But Wagner’s recent victory in Bakhmut after a grueling monthslong battle has given Mr. Prigozhin political carte blanche, said Dmitri Oreshkin, a Russian political scientist and Kremlin critic.

“You are given everything, permission to break the law, to take people from prisons without asking anyone’s permission, to kill those people if you don’t like them for discipline,” Mr. Oreshkin said about the terms of the deal between Mr. Putin and Mr. Prigozhin. “If he had not brought this victory, he would have been torn apart” by the elites he has been disparaging.

“For him it was a matter of life and death.”

Milana Mazaeva contributed reporting.

Fighters aligned with Ukraine warn of additional attacks inside Russia.

Military analysts suggested the cross-border attack this week was aimed at forcing Russia to divert troops for border defense from the front in southeastern Ukraine ahead of a planned Ukrainian counteroffensive, and to embarrass President Vladimir V. Putin’s government.

Images verified by The New York Times showed armored vehicles with Ukrainian markings driving in the Belgorod region of southern Russia and smoke from explosions billowing over farm fields. Two groups calling themselves armed Russian opposition organizations, the Free Russia Legion and the Russian Volunteer Corps, claimed responsibility.

The raid was the most disruptive, direct ground assault on Russian territory during the war, staged from an area of northern Ukraine that the Ukrainian Army freed from Russian occupation last spring. Kyiv denied directing the assault and said only Russian citizens crossed the border in the raid.

The commanders and soldiers stood, toting machine guns, some with camouflage fabric bands pulled over their faces, in front of an armored personnel carrier that they said they had captured and driven out of Russia. That could not be independently confirmed.

They called the two-day incursion a success. “We saw the military and political leadership of Russia are absolutely not prepared” for an attack, the commander said. “When it came to action, everything fell apart.”

Analysts of Russian politics said the attack could stir discontent over Russian military capabilities among the country’s pro-war groups but could also help Mr. Putin with a rally-around-the-flag effect. Already, the Kremlin has said that the raiders had abandoned American-made military vehicles inside Russia, and Moscow can use the far-right histories of some of the raiders to bolster its largely false claim to be fighting Nazis in Ukraine.

The Kremlin, eager to discredit the renegade Russians, dismissed them on Wednesday as neo-fascists.

One commander of the Russian Volunteer Corps, Denis Kapustin, is a known far-right extremist. The Anti-Defamation League has said that he was involved in the Mixed Martial Arts world in Europe and that he has trained younger members of the far-right National Democratic Party of Germany. At the news conference on Wednesday, he introduced himself to reporters by his call sign, White Rex.

Asked about his ultranationalist ideology Mr. Kapustin described himself as right wing and said that his views were “traditionalist” and “patriotic.”

Sergei K. Shoigu, Russia’s defense minister, called the raid a terrorist act. “In response to similar action by Ukrainian fighters, we will respond in an operational manner and very harshly,” he told a gathering of security officials in Moscow, Russian media reported on Wednesday.

The Ukrainian military, he said, had been aware of the groups’ intentions ahead of the raid, helped in the planning, and provided gasoline for vehicles and medical care for wounded soldiers.

“Everything we do within the state borders of Ukraine we obviously coordinate with the Ukrainian military,” he said. “Everything we do, every decision we make, beyond the state border, is our decision.”

The Ukrainian military, he said, had “wished us good luck” but not crossed the border into Russia, echoing what Ukrainian officials had said.

Another commander, who asked to be identified by the nickname Cesar, said Russia’s military had been slow to respond with reinforcements after the group drove armored personnel carriers across the border and attacked a border post. “The reaction was slow, panicked, disorganized and didn’t begin for hours,” he said.

Cesar said the Free Russia Legion had driven American-made armored vehicles but said they were not provided by the Ukrainian military. The group had bought them, he said. He said his group suffered losses in the fighting but declined to say how many soldiers had been killed or wounded.

White Rex said his group, the Russian Volunteer Corps, had not used any American-made vehicles in the assault.

The news conference organizers kept a strict time limit, lest the gathering be targeted by a Russian missile. After about 40 minutes, the soldiers drove away in pickup trucks and, with a rumble of a diesel engine, the armored personnel carrier they said they had captured.

Evelina Riabenko contributed reporting.

Russia and Belarus sign an agreement ‘determining the procedure’ for storing nuclear weapons in Belarus.

Mr. Putin has repeatedly issued veiled threats of the use of nuclear weapons since launching the full-scale invasion of Ukraine last year. U.S. officials say they have seen no effort by Russia to move or employ its nuclear weapons, but worries remain.

It was not clear whether Mr. Putin would transfer nuclear weapons into Belarus, and he was vague on the timeline for any such move in his March comments. Even if Russia were to move some of its nuclear assets to Belarus, it would not seriously change the nuclear threat since Russia can already target a broad range of territory from within its own borders.

— The New York Times

Zelensky asks Iranians to stop backing  Russia.

Mr. Zelensky and Ukraine’s allies have accused Iran of supplying a long-range attack drone, the Shahed-136, to Russia since the start of the war last year. Iran has denied the allegation. The drones have become a mainstay of Russia’s near nightly attacks on Ukrainian cities, and Ukrainian forces say they shot down 36 of them on Thursday morning alone.

Ukraine’s relationship with Iran has long been stymied by Iran’s alliance with Russia, which illegally annexed Crimea after invading in 2014. The leaders of Iran and Russia both view the United States as an enemy and a threat to their grip on power.

It’s not the first time Mr. Zelensky has used his speeches to address the people of other countries directly. In a speech in the early days of the war, he asked the Russian people — in Russian — to oppose the war.

Relations between Iran and Ukraine deteriorated when two missiles fired by Iranian military forces downed a Ukrainian jetliner in January 2020, killing all 176 passengers and crew on board. Iran has said it was an accident.

The relationship soured further following Russia’s full-scale invasion of Ukraine last year. A few months into the war, U.S. officials say, Iran supplied military drones to Russia. Iran denied the shipments, only admitting to sending drones to Russia before the war began. In December, Mr. Zelensky, in an address to Congress, accused Iran of conspiring with Russia by sending hundreds of drones, including the Shahed-136.

That weapon is launched from a truck, flies autonomously for up to 1,500 miles, dives toward its target and explodes on impact. Its slow speed and low altitude make it easy to target, British defense officials have said.

A U.S. aircraft carrier visits Oslo, in a show of strength aimed at Russia.

The Russian Embassy said on its Facebook page Wednesday that “there are no questions in the north that require a military solution.” Since Russia, the embassy said, “poses no direct military threat to Norway, such demonstrations of power appear illogical and harmful.”

Jonas Gahr Store, Norway’s prime minister, said through a spokesperson that the carrier’s presence in Oslo transcends mere symbolic value. It also reflects, he said, the United States’ power at sea.

Historically, Norway has been slightly reluctant to allow a strong U.S. military presence, but its stance has slowly changed since Russia illegally seized the Crimean peninsula from Ukraine in 2014. American Marines have trained on a rotational basis in Norway since 2017, buttressing their defenses against a resurgent Russia, and in 2018 U.S. troops joined 50,000 Allied Forces in the Trident Juncture, NATO’s largest military exercise since the end of the Cold War in 1991.

Andreas Osthagen, a senior research fellow at the Fridtjof Nansen Institute in Norway and an expert on geopolitical issues related to the Arctic, called the trip part of a trend of the U.S. military engaging in the Arctic and North Atlantic, not only a response to Russian aggression in Europe, but also the increasing Chinese presence in the Arctic.

After its stay in Oslo, the carrier is scheduled to move along Norway’s coast into the Norwegian Sea, but the Norwegian Armed Forces did not say precisely where or for how long. The aircraft carrier, the armed forces said, will train with Norway’s military.

— Henrik Pryser Libell

A unit of Ukraine’s security services likely orchestrated the Kremlin drone attack, U.S. officials say.

U.S. officials say their level of confidence that the Ukrainian government directly authorized the Kremlin drone attack is “low” but that is because intelligence agencies do not yet have specific evidence identifying which government officials, Ukrainian units or operatives were involved.

The attack appeared to be part of a series of operations that have made officials in the United States — Ukraine’s biggest supplier of military equipment — uncomfortable. The Biden administration is concerned about the risk that Russia will blame U.S. officials and retaliate by expanding the war beyond Ukraine.

American spy agencies see an emerging picture of a loose confederation of Ukrainian units able to conduct limited operations inside and outside Russia, either by using their own personnel or partners working under their direction. Some of these missions could have been conducted with little, if any, oversight from Mr. Zelensky, officials said.

In addition to the drone attack, U.S. officials say they believe the Ukrainians were responsible for the assassination of the daughter of a prominent Russian nationalist, the killing of a pro-Russian blogger and a number of attacks in Russian towns near the border with Ukraine, the most recent of which occurred Monday.

American officials similarly view the attack on the Nord Stream pipelines — which carried natural gas from Russia to Europe — as the work of pro-Ukrainian operatives whose ties to the Ukrainian government have yet to be determined.

The officials, who spoke on the condition of anonymity to discuss sensitive intelligence, described their assessment in broad terms, but would not share the details of the intercepts. Representatives for the White House, the Central Intelligence Agency and the Office of the Director of National Intelligence declined to comment.

Though the drone attack caused little damage, it punctured the sense of security and invincibility the Kremlin has sought to portray within Moscow despite the chaos it has created with its war in Ukraine.

U.S. intelligence agencies’ ability to determine responsibility for attacks against Russian targets has been complicated by the way Ukraine has organized its security services, which have secretive, overlapping and sometimes competing responsibilities.