Vladimir V. Putin is known for his tight control over the news media in Russia. His onetime ally, the Wagner military group founder Yevgeny V. Prigozhin, is himself the owner of a conservative media outlet and a flamboyant showman on social media.

But it was an unlikely figure who emerged with a public relations victory in the wake of Mr. Prigozhin’s mutiny: the longtime dictator of Belarus, the neighboring country that is firmly in Moscow’s orbit.

The Belarusian leader, Aleksandr G. Lukashenko, is viewed largely as the Kremlin’s docile satrap. But on Sunday, he took credit for brokering an agreement between Mr. Putin and Mr. Prigozhin, averting a scenario that the Russian leader had compared to the civil war that followed the Revolution of 1917.

Now Mr. Lukashenko, an international pariah, is trying to use the P.R. victory to burnish his credentials as a credible statesman, mediator — and above all, loyal ally to Mr. Putin.

Late on Saturday evening, as fears were heightening over a potential clash between Wagner troops, who were within 125 miles of Moscow, and Russian soldiers, Mr. Lukashenko’s press service issued an announcement: The Belarusian president had found “an absolutely profitable and acceptable option for resolving the situation.”

Shortly thereafter, Mr. Prigozhin announced that a column of his fighters that had ridden about 500 miles from southern Russia was turning around and going home.

As part of the deal, the criminal case opened against Mr. Prigozhin for organizing an armed insurrection would be dropped, Wagner troops would not face charges and Mr. Prigozhin would leave Russia for Belarus, the Kremlin’s spokesman said. His whereabouts on Sunday was not known.

What, if any, promises were made on behalf of the Kremlin, Wagner or Mr. Lukashenko remain unclear. But Mr. Lukashenko’s state-controlled media quickly switched into high gear to portray his efforts to defuse the conflict as evidence of statesmanship.

The state news agency, Belta, reported that on Saturday morning — as Mr. Putin faced “the most acute phase of the situation in Russia” — he phoned his Belarusian counterpart in Minsk.

Mr. Putin “was skeptical about the possibility of negotiations and doubted whether Yevgeny Prigozhin would pick up the phone, since at that time he did not talk to anyone,” a Belarusian government propagandist, Vadim Gigin, told pro-Kremlin media on Sunday, in an interview that was covered extensively by Belta.

But Mr. Putin agreed to mediation, and when “the president of Belarus called, Yevgeny Prigozhin immediately picked up the phone,” said Mr. Gigin, on whom the European Union once imposed sanctions for “supporting and justifying repression against the democratic opposition and civil society.”

The conversation between Mr. Lukashenko and Mr. Prigozhin was “very difficult,” said Mr. Gigin, who this month became the director of the National Library of Belarus. “They immediately blurted out such vulgar things it would make any mother cry. The conversation was hard, and as I was told, masculine.”

Though other possible explanations have been advanced for why Mr. Prigozhin gave up on his “march for justice” to Moscow, some offering minimal credit to Mr. Lukashenko, the Belarusian media machine has been trumpeting his role as a power broker, a rare role reversal at a time when the dictator has become overwhelmingly dependent on Russia.

“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 — first in the eyes of Putin, in the eyes of the international community as a mediator or negotiator, and as a possible guarantor of the deal.”

Mr. Lukashenko has managed to hold onto power for 29 years, but at a cost. He has increasingly allowed Belarus to become a vassal state of Russia, especially after getting Moscow’s backing in 2020, when he violently crushed a democracy movement challenging his claim that he had won an election in a landslide.

Dependent on Moscow not just for political support but also for economic viability, Belarus allowed Mr. Putin to use it as a staging ground for his full-scale invasion of Ukraine in February 2022, and as a storage site for Russian tactical nuclear weapons.

Details have also emerged that Belarus has participated in Russia’s practice of taking children out of Russian-occupied territories in Ukraine and bringing them to so-called summer camps. The International Criminal Court has issued warrants for Mr. Putin and his children’s rights commissioner, and Ukrainian prosecutors are reviewing evidence that children have been brought to three camps in Belarus, including at least one belonging to a state-owned company.

Opposition leaders believe that Mr. Putin’s ambitions are not limited to Ukrainian territory. Eventually, they predict, he will try to strengthen his control over Belarus.

With his reported mediation in the Wagner crisis, Mr. Lukashenko may hope to reclaim some of his rapidly eroding sovereignty, and stem Belarusian fears of being swallowed by its larger neighbor, said Dmitri Avosha, the founder of the Belarusian website Tribuna.

“Lukashenko simply did a favor to Putin in its purest form, and helped himself solve the problem of occupation,” he said.

It is not the first time Mr. Lukashenko also tried to claim the mantle of mediator.

He did so in 2014 and 2015, after an earlier Russian foray into Ukraine, when Moscow backed separatists in the eastern Donbas region. He tried again shortly after the full-scale invasion, dragooning delegations from Moscow and Kyiv to the southeastern city of Gomel, but the talks quickly fell apart.

Many observers are now raising questions about whether Mr. Prigozhin would be safe from the threat of kidnapping or assassination in Belarus, given Mr. Putin’s openly expressed anger at him.

Even before 2020, when Mr. Lukashenko became still more a Putin puppet, Russian special services sometimes entered Belarus’ territory to capture its enemies, said Mr. Slunkin, the European Council analyst. “And now, they will just do what they want.”

However much the balance of power between Mr. Lukashenko and Mr. Putin may have shifted now, both men still need each other to remain in power.

“They are two Siamese twins,” said Pavel Latushka, a former Belarusian diplomat and minister now in exile. “They can’t live without each other. It’s one body, two heads. The fall of one means the political death of another.”