Confusion and uncertainty pervaded Russia on Sunday, with neither President Vladimir V. Putin nor Yevgeny V. Prigozhin, the head of a mutinous mercenary group, appearing anywhere in public a day after the most profound government crisis in three decades — an open military rebellion — appeared defused.

Even as state television tried to trumpet the fact that Russian unity and “maturity” had prevailed, independent commentators assessing the damage concluded that Mr. Putin’s aura of infallibility and invincibility had been punctured. And some wondered aloud why much of Russia’s leadership was being neither seen nor heard.

Aside from Mr. Putin, neither Sergei K. Shoigu, the minister of defense, nor Valery V. Gerasimov, the military chief of staff, had put in a public appearance since the uprising started on Friday night. Many heads of the country’s security services also proved invisible.

“Where was the leadership of the Ministry of Defense during the approach of the armed unit to Moscow?” wrote Yuri Kotenok, one of a small tribe of influential military bloggers who have emerged as a supportive if critical voice regarding the war in Ukraine. Could a foreign enemy, he asked, march with equal ease on the capital?

World leaders also chimed in. Secretary of State Antony J. Blinken said on Sunday that Mr. Prigozhin’s rebellion had revealed cracks in Mr. Putin’s hold on power. “It was a direct challenge to Putin’s authority,” Mr. Blinken said on CBS’s “Face the Nation.’’

In the end, Mr. Prigozhin, the head of the mercenary force known as Wagner, called off his men after staging an armed uprising against the military’s leadership for nearly 24 hours this weekend. But the damage had been done, not least because his blistering criticism of the military leaders as incompetent included questioning the Kremlin’s justifications for invading its neighbor in the first place.

Russians — and the world — had watched with alarm as his columns of armored vehicles inched ever closer to Moscow with little armed opposition, posing a threat to Mr. Putin and raising the specter of a civil war in the nuclear-armed state.

“Putin and the state have been dealt a severe blow,” wrote Tatiana Stanovaya, the founder of the political analysis firm R.Politik. She predicted it would have significant repercussions for the regime.

Ms. Stanovaya noted that Mr. Prigozhin had reversed course only after Mr. Putin, a longtime ally, expressed fury at what the president described as a “stab in the back.” Mr. Prigozhin, she wrote, ”found himself unprepared to assume the role of a revolutionary.”

“He also wasn’t prepared for the fact that Wagner was about to reach Moscow, where his only option remained — to ‘take the Kremlin’ — an action that would inevitably result in him and his fighters being eradicated,” Ms. Stanovaya wrote.

A new analysis by a FilterLabs.AI, a firm that tracks public sentiment in Russia by monitoring social media and internet forums, found that Mr. Prigozhin was also subjected to a Kremlin propaganda assault. And access to Telegram channels that were controlled by Mr. Prigozhin or supportive of him became more difficult, with users reporting slowdowns.

Public support for Mr. Prigozhin and Wagner fell sharply, FilterLabs found.

“For Prigozhin’s campaign to have worked, he would have needed to see high support in Moscow,” the FilterLabs analysis said. “This did not materialize, despite his own base of support and media campaigns.”

Instead a deal was reached.

The Wagner forces would turn around, and Mr. Prigozhin could go to neighboring Belarus and avoid criminal charges. The Wagner fighters, too, would be absolved.

The Kremlin spokesman, Dmitri S. Peskov, said the agreement had been struck to “avoid bloodshed, to avoid an internal confrontation, to avoid clashes with unpredictable consequences.” He did not indicate that the uprising would lead to any changes in the Russian military leadership, as Mr. Prigozhin had demanded, and said that Russia’s military operations in Ukraine would continue unchanged.

The deal that defused the hostilities was credited to Belarus’s leader, Aleksandr G. Lukashenko, a Putin ally. Had Mr. Putin fallen, of course, Mr. Lukashenko would also have been vulnerable, so in aiding his patron, he was also aiding himself.

“Putin lost because he showed how weak his system is, that he can be challenged so easily,” said Pavel Slunkin, a former Belarusian diplomat and analyst at the European Council on Foreign Relations. “Prigozhin challenged, he attacked, he was so bold and then he retreated, looking like a loser. Only Lukashenko won points.”

The rebellion, even if aborted, may now affect Russia’s global standing as partners like China reassess the strength of Mr. Putin’s authority.

Mr. Prigozhin proved uncharacteristically quiet on Sunday, a day after he was seen driving away from the military headquarters in the southwestern city of Rostov-on-Don that his forces had seized during the uprising. An independent Russian broadcaster who asked Mr. Prigozhin’s spokesman for comment was told that he was unavailable, but that he would soon start responding to the press.

It was unclear how safe Mr. Prigozhin might be in Belarus, given Mr. Putin’s track record of pursuing those whom he believes betrayed him, whether in Russia or abroad. As if to emphasize this point, Vesti Nedelu, the Kremlin’s signature weekly television show, broadcast an old clip on Sunday of Mr. Putin saying that the one thing he could never forgive was “betrayal.” A guest on another prominent talk show called for Mr. Prigozhin and his top military commander to be executed.

Beyond that, Mr. Prigozhin’s ambitions as a military leader might clash with the goals of Mr. Lukashenko, who has tried to keep his country out of the war.

“It will be dangerous for Lukashenko to have Wagner in Belarus,” said Dmitry Bolkunets, a Belarusian political scientist who taught at an elite Moscow university before becoming an opposition activist.

“Prigozhin is a Z patriot,” Mr. Bolkunets said, referring to the letter that has come to symbolize the conflict in Ukraine. “He is a guy who supports the war, who wants an empire, and Lukashenko is afraid of the empire.”

Wagner fighters were seen streaming out of Rostov-on-Don, the military hub, to the sound of residents chanting the group’s name. It was unclear where they were headed.

The group of mercenaries that spearheaded some of Russia’s most effective military campaigns in Ukraine said they had already been facing a choice: to submit to, and be controlled by, the country’s Defense Ministry — an agency they openly despise — or be disbanded.

Nikolai A. Pankov, Russia’s deputy defense minister, said on June 10 that the country’s numerous “volunteer regiments” would have to sign contracts with the ministry by the end of the month. Days later, Mr. Putin told a group of pro-military bloggers that the contracts should be signed as soon as possible.

Mr. Prigozhin had no intention of bowing to the Russian military commanders he had frequently accused of corruption and incompetence. “No one will sign the contracts,” he said in a statement on June 14.

On Sunday, it was unclear if that held true.

For Ukraine, although the upheaval could strain Russia’s war effort, analysts thought it would create less of an opportunity than if the Russian military had been forced to withdraw reserve units from the front to protect Moscow.

Attacks continued. Russian shelling hit a five-story apartment building before dawn in Ukraine’s southern region of Kherson, killing a 44-year-old man and trapping a woman under the rubble, local officials said.

President Volodymyr Zelensky of Ukraine seized on the brief rebellion to reemphasize his message that his country is fighting an unstable neighbor on behalf of all of Europe.

“Today the world saw that the bosses of Russia do not control anything,” Mr. Zelensky said in a video address late on Saturday. “Nothing at all. Complete chaos. Complete absence of any predictability.”

Mr. Zelensky mocked Mr. Putin, without naming him.

“I will say it in Russian: The man from the Kremlin is obviously very afraid and probably hiding somewhere, not showing himself,” he said.

Reporting was contributed by Julian E. Barnes, Valerie Hopkins, Ivan Nechepurenko, Anton Troianovski, Matthew Mpoke Bigg, John Ismay, Alina Lobzina and Milana Mazaeva.

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