President Vladimir V. Putin long styled himself as Russia’s guarantor of stability and the uncompromising protector of its statehood.

This weekend, Russian stability was nowhere to be found, and neither was Mr. Putin, who after making a brief statement on Saturday morning vanished from sight during the most dramatic challenge to his authority in his 23-year reign.

In his absence, he left stunned Russians wondering how the leader of a paramilitary group, Yevgeny V. Prigozhin, 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 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. With Saturday’s events, he said, Mr. Putin had conclusively lost his status as the guarantor of the elite’s wealth and security.

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 it is the security of the Russian state that Mr. Putin describes as his guiding motivation for invading Ukraine.

Even amid the 16-month war in Ukraine, the Kremlin has been focused on normalcy at home. Mr. Putin has resisted hard-line calls to declare martial law or to close the country’s borders. 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. The leader of the Wagner paramilitary group, Mr. Prigozhin had his forces seize a Russian military headquarters in the south, then sent a column of troops north toward Moscow, vowing to enter the capital. The crisis was defused late Saturday, when Mr. Prigozhin agreed to pull back his forces in a deal that allowed him and his troops to avoid prosecution.

The immediate threat was averted. But in the process, Mr. Putin lost more than his reputation for providing stability: The fact that Mr. Prigozhin and his forces were not being punished punctured the Russian leader’s reputation as a decisive leader who would not tolerate disloyalty.

That impression was compounded by reports from Russian military bloggers that Prigozhin forces had shot down Russian combat aircraft. Mr. Putin also called Mr. Prigozhin a traitor after he launched his insurrection — and after the mercenary chieftain questioned Mr. Putin’s very rationale for the war in Ukraine.

Experts said this made Mr. Putin look less in control of the Russian state than previously known. And foreign adversaries were quick to seize on that theme.

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

One of the more confounding aspects of the crisis was why Mr. Putin allowed Mr. Prigozhin’s very public conflict with Russia’s Defense Ministry to escalate for months without addressing it. Mr. Prigozhin had been brazenly outspoken for months in assailing and belittling the Russian military’s leadership.

Two people close to the Kremlin, speaking on condition of anonymity, described the crisis as first and foremost the product of a dysfunctional system of governance verging on chaos — vividly captured in the Russian word bardak.

Decisions on how to handle Mr. Prigozhin’s uprising were made on the fly Saturday, they said, after months in which the president and his inner circle kept on kicking the can down the road rather than finding a way to deal with the iconoclastic mercenary chief.

“This was a rather neglected issue,” Konstantin Zatulin, a senior member of Parliament in Mr. Putin’s United Russia party, said in an interview. The risk posed by Mr. Prigozhin, he went on, “wasn’t diagnosed in time — maybe in the hope that it would work itself out on its own.”

Mr. Zatulin argued that Mr. Putin did, in the end, provide stability, because he blessed a deal to end the uprising and averted a pitched battle outside Moscow. But he acknowledged that the drama made no one look good — it “didn’t add to anyone’s authority.”

“This is proof that there is a problem,” Mr. Zatulin said. “And in a wartime moment to demonstrate problems so publicly — that is damaging, of course.”

For Mr. Putin himself, the mutiny could spark an “existential crisis,” said Sergei Markov, a political analyst and former Kremlin adviser.

“What he always took pride in is the solidity of Russian statehood and political stability,” Mr. Markov said. “That’s what they loved him for. And it turns out that it doesn’t exist.”