The rebellious mercenary soldiers who briefly took over a Russian military headquarters on an ominous march toward Moscow were gone Sunday, but the short-lived revolt looks to have weakened President Vladimir Putin just as his forces are facing a fierce counteroffensive in Ukraine.

Under terms of the agreement that ended the crisis, Yevgeny Prigozhin, who led his Wagner troops in the failed uprising, will go into exile in Belarus but will not face prosecution.

Yet it was unclear what would ultimately happen to him and his forces. Few details of the deal were released either by the Kremlin or Belarusian President Alexander Lukashenko, who brokered it. Neither Mr. Prigozhin nor Mr. Putin have been heard from, and top Russian military leaders have also remained silent.

U.S. Secretary of State Antony Blinken described the weekend’s events as “extraordinary,” recalling that 16 months ago Mr. Putin appeared poised to seize the capital of Ukraine and now he has had to defend Moscow from forces led by his onetime protege.

“I think we’ve seen more cracks emerge in the Russian facade,” Mr. Blinken said on NBC’s “Meet the Press.”

“It is too soon to tell exactly where they go and when they get there, but certainly we have all sorts of new questions that Putin is going to have to address in the weeks and months ahead.”

It was not yet clear what the fissures opened by the 24-hour rebellion would mean for the war in Ukraine. But it resulted in some of the best forces fighting for Russia being pulled from the battlefield: the Wagner troops, who had shown their effectiveness in scoring the Kremlin’s only land victory in months, in Bakhmut, and Chechen soldiers sent to stop them on the approach to Moscow.

The Wagner forces’ largely unopposed, rapid advance also exposed vulnerabilities in Russia’s security and military forces. The mercenary soldiers were reported to have downed several helicopters and a military communications plane. The Defense Ministry has not commented.

“I honestly think that Wagner probably did more damage to Russian aerospace forces in the past day than the Ukrainian offensive has done in the past three weeks,” Michael Kofman, director of Russia studies at the CNA research group, said in a podcast.

Ukrainians hoped the Russian infighting could create opportunities for their army, which is in the early stages of a counteroffensive to take back territory seized by Russian forces.

“Putin is much diminished and the Russian military, and this is significant as far as Ukraine is concerned,” said Lord Richard Dannatt, former chief of the general staff of the British armed forces. “...Prigozhin has left the stage to go to Belarus, but is that the end of Yevgeny Prigozhin and the Wagner Group?”

Under terms of the agreement that stopped Mr. Prigozhin’s advance, Wagner troops who didn’t back the revolt will be offered contracts directly with the Russian military, putting them under the control of the military brass that Mr. Prigozhin was trying to oust. A possible motivation for Mr. Prigozhin’s rebellion was the Defense Ministry’s demand, which Mr. Putin backed, that private companies sign contracts with it by July 1. Mr. Prigozhin had refused to do it.

“What we don’t know, but will discover in the next hours and days is, how many of his fighters have gone with him, because if he has gone to Belarus and kept an effective fighting force around him, then he...presents a threat again” to Ukraine, Mr. Dannatt said.

Ukrainian President Volodymyr Zelenskyy said he told U.S. President Joe Biden in a phone call on Sunday that the aborted rebellion in Russia had “exposed the weakness of Putin’s regime.”

In their lightning advance, Mr. Prigozhin’s forces on Saturday took control of two military hubs in southern Russia and got within 120 miles of Moscow before retreating.

People in Rostov-on-Don cheered Wagner troops as they departed late Saturday, a scene that played into Mr. Putin’s fear of a popular uprising. Some ran to shake hands with Mr. Prigozhin as he drove away in an SUV.

Yet the rebellion fizzled quickly, in part because Mr. Prigozhin did not have the backing he apparently expected from Russian security services. The Federal Security Services immediately called for his arrest.

“Clearly, Prigozhin lost his nerve,” retired U.S. Gen. David Petraeus, a former CIA director, said on CNN’s “State of the Union.”

“This rebellion, although it had some applause along the way, didn’t appear to be generating the kind of support that he had hoped it would.”

Rostov appeared calm Sunday morning, with only tank tracks on the roads as a reminder of the Wagner fighters.

“It all ended perfectly well, thank God. With minimal casualties, I think. Good job,” said a resident, who agreed only to provide his first name, Sergei. He said the Wagner soldiers used to be heroes to him, but not now.

In the Lipetsk region, which sits on the road to Moscow, residents appeared unfazed by the turmoil.

“They did not disrupt anything. They stood calmly on the pavement and did not approach or talk to anyone,” Milena Gorbunova told the AP.

As Wagner forces moved north toward Moscow, Russian troops armed with machine guns set up checkpoints on the outskirts. By Sunday afternoon, the troops had withdrawn and traffic had returned to normal, although Red Square remained closed to visitors. On highways leading to Moscow, crews repaired roads ripped up just hours earlier in panic.

Anchors on state-controlled television stations cast the deal ending the crisis as a show of Mr. Putin’s wisdom and aired footage of Wagner troops retreating from Rostov to the relief of local residents who feared a bloody battle for control of the city. People there who were interviewed by Channel 1 praised Mr. Putin’s handling of the crisis.

But the revolt and the deal that ended it severely dented Mr. Putin’s reputation as a leader willing to ruthlessly punish anyone who challenges his authority.

Mr. Prigozhin had demanded the ouster of Defense Minister Sergei Shoigu, whom Mr. Prigozhin has long criticized in withering terms for how he has conducted the war in Ukraine.

The U.S. had intelligence that Mr. Prigozhin had been building up his forces near the border with Russia for some time. That conflicts with Mr. Prigozhin’s claim that his rebellion was a response to an attack on his field camps in Ukraine on Friday by the Russian military that he said killed a large number of his men. The Defense Ministry denied attacking the camps.

U.S. Rep. Mike Turner, who chairs the House Intelligence Committee, said Mr. Prigozhin’s march on Moscow appeared to have been planned in advance.

“Now, being a military guy, he understands the logistics and really the assistance that he’s going to need to do that,” including from some Russians on the border with Ukraine who supported him, Mr. Turner said on CBS’ “Face the Nation.”

“This is something that would have had to have been planned for a significant amount of time to be executed in the manner in which it was,” he said.

This report contains information from The Associated Press.