Its leader is officially dead, as is its founding commander. President Vladimir V. Putin of Russia is claiming it doesn’t exist.

Wagner, the once-powerful Russian private military company that fell out of favor with the Kremlin after an aborted mutiny in June, has been cast into even greater uncertainty since Wednesday, when its leader, Yevgeny V. Prigozhin, died in a plane crash.

The Russian authorities said Sunday that DNA tests, conducted on bodies recovered from the site in the Tver region, confirmed that Mr. Prigozhin and nine other people listed on plane’s manifest had died in the suspicious crash.

Now attention is shifting to whether Wagner, which Mr. Prigozhin built over nearly a decade into a global empire that benefited Moscow as well as his own wallet, ultimately will die, too.

U.S. and Western officials say that the Kremlin is considering ways to bring Wagner under more direct control of the Russian state but hasn’t made any final decisions on what to do with the group.

It is unlikely that Russia wants to squander the trained fighters, geopolitical inroads and business interests that Mr. Prigozhin cultivated since Wagner’s founding in 2014. His outfit has operated in at least 10 countries.

But finding a way to neutralize an armed organization that posed one of the biggest threats to Mr. Putin’s tenure in 23 years, while also retaining its fighting power and global links, is a difficult task, particularly given the longstanding enmity between fighters with the private military company and the leadership of the Russian Defense Ministry.

“I think that PMC Wagner, in itself, as a structure, most likely won’t exist,” Aleksandr Borodai, a member of the Russian Parliament who briefly served as a Moscow-installed proxy leader in Donetsk, Ukraine, in 2014, said in a phone interview.

Mr. Borodai said Wagner fighters would continue to fight and were already joining volunteer formations, as well as official units, under the Russian armed forces.

“There are many of them,” Mr. Borodai said. “It’s a big flow. The flow didn’t start yesterday, and it won’t end tomorrow. People are coming in, they will continue to fight, they have experience.”

“As for the future of PMC Wagner, I don’t know,” he said. “But there probably won’t be one.”

Mr. Putin has sent mixed signals on his plans.

During a meeting at the Kremlin after the mutiny in late June, Mr. Putin told Wagner commanders they could continue serving together under different leadership, he said last month in an interview with the Russian newspaper Kommersant.

Mr. Putin recounted how he proposed that the commanders keep serving under a Kremlin-approved former Wagner member who uses the alias Gray Hair. Mr. Putin said Mr. Prigozhin refused on his commanders’ behalf, even though some shook their heads in agreement.

In the same interview, Mr. Putin also said Wagner doesn’t exist, because Russian law doesn’t permit private military companies.

The Kremlin spokesman Dmitri S. Peskov has made similar remarks, which appear to be aimed at signaling that the group, as it stands, has no future in Russia.

Wagner theoretically could still function without Mr. Prigozhin and its founding commander, Dmitri V. Utkin, who the Russian authorities also confirmed died in the plane crash, alongside five other passengers connected to Wagner and three crew members.

The mercenary group has what its affiliated Telegram channels describe as a “council of commanders,” who oversee operational matters day to day. Several members of the council were not on Mr. Prigozhin’s plane.

None of those Wagner commanders has appeared in public or issued a statement since the crash, despite repeated promises of a coming announcement on Wagner-affiliated Telegram channels. It is unclear whether those commanders would have the Russian political capital to operate the larger Wagner operation, as other elites probably begin circling Mr. Prigozhin’s more lucrative assets.

At a makeshift sidewalk memorial to the fallen Wagner leaders near Red Square in Moscow, fighters who went to pay their respects said they were sure that the private military company would continue operating.

“Utkin and Prigozhin are not the whole leadership,” a 36-year-old Wagner volunteer who gave only his call sign, Adzhit, said, after he placed a bouquet of white lilies in a plastic vase on the memorial.

“If you know the internal structure of Wagner, you can understand one thing: The loss of one, two, or three will not affect the effectiveness of this formation in any way,” he said.

Still, without the Kremlin’s clear imprimatur, the group’s operations risk falling apart. Mr. Prigozhin’s personal connection to Mr. Putin dating to the 1990s in St. Petersburg, Russia, served as a calling card abroad, allowing the tycoon to peddle geopolitical power alongside security services in Mali, the Central African Republic, Libya and other nations.

Even after the mutiny, Mr. Prigozhin, who handled the business side of the group, was flying to locations in Africa trying to reassure clients and continue operations. His interests spanned oil, gas, precious metals and stones, Mr. Putin said this past week, noting that the tycoon returned from Africa to meet certain officials the day before boarding the ill-fated private jet in Moscow. His travels came amid reports that the Russian Defense Ministry was trying to assert direct control over some of his foreign operations.

Catrina Doxsee, an associate fellow at the Center for Strategic and International Studies, said she expected the model that Mr. Prigozhin developed — using a shadowy parastatal organization to advance international interests but also do business — to continue in some form in Russia. But she suspected that future such operations might be more fractured.

“One of the big things the mutiny in June demonstrated was the problem for Putin in allowing one company, and really one man, to hold the monopoly of power and of knowledge over all of these different operations,” Ms. Doxsee said.

She said that going forward there could be “many different actors fulfilling these roles, rather than one monopoly.”

Mr. Putin is also likely to ensure that any subsequent operations avoid the kind of enmity with the Russian military leadership that Mr. Prigozhin cultivated.

Aleksei A. Venediktov, who headed the liberal radio station Echo of Moscow before the Kremlin shut it down last year, said the events in recent days represented a “very important response to the Russian military elite.”

He said Mr. Putin was communicating, “You are the ones most important to me. You thought I’d let this guy tear you apart. No,’” adding that he was relaying, “I’m commander in chief, and you’re my loyal soldiers.”

Wagner built up a visible domestic brand in Russia only after Mr. Putin’s full-scale invasion of Ukraine last year. Wagner recruited heavily from the Russian population, as well as from Russian prisons, and was lauded on Russian state news during its campaign to take the Ukrainian city of Bakhmut.

The publicity came alongside social media commentaries from Mr. Prigozhin, who previously operated largely in anonymity. The change fed the tycoon’s ego and gave him public standing, making it harder for the Kremlin to eradicate the group completely.

A trio of Wagner soldiers in camouflage who visited the makeshift memorial in Moscow insisted that Wagner was not going to be disbanded.

“We are all standing by, we have not betrayed anyone, we have not abandoned anyone, and we will stand to the last,” said one of the soldiers, who gave his call sign as Prapor, short for Ensign.

When asked if he would switch contracts from Wagner to the Russian Defense Ministry, Prapor did not answer.

“We have one contract,” he said. “And that is a contract with the motherland.”

Anton Troianovski, Julian E. Barnes and Eric Schmitt contributed reporting.

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