In his first remarks since his revolt, Prigozhin claims he wasn’t trying to overthrow Putin.

According to Russian media reports published on Monday, the criminal case against Mr. Prigozhin remains open and the charges against him have not been dropped. Kommersant, a Russian newspaper, and the country’s three main news agencies — Tass, RIA and Interfax — all reported that the Federal Security Service, or F.S.B., continued to investigate.

The publications, all either state-controlled or affiliated with the Kremlin, cited anonymous sources, so their reports could not be independently verified. If the proceedings continue, Mr. Prigozhin could face up to 20 years in prison.

Even if the case is dropped, critics of Belarus’s president, Aleksandr G. Lukashenko, have raised doubts over whether Mr. Prigozhin would be safe there, given the government’s close ties to Mr. Putin, who has been a crucial source of support for Mr. Lukashenko.

Mr. Prigozhin was last seen in public late Saturday, smiling and shaking hands with supporters when he left the southern Russian city of Rostov-on-Don after he called an end to his brief uprising and turned back the column of soldiers he had sent on a march to Moscow.

Since then, his location has been unknown. On Sunday evening, Mr. Prigozhin’s press service told RTVI, a Russian TV channel, that he “says hi to everyone and will answer questions” when he has good cellphone reception.

Despite the severity of Mr. Prigozhin’s actions over the weekend, some Russian officials have been reluctant to criticize Wagner fighters, who have proven themselves to be effective, if brutal, in fighting on Russia’s behalf in Ukraine and in other conflicts.

Andrei Kartapolov, the chairman of the Russian Parliament’s defense committee, said Sunday that the Wagner fighters who took over the army headquarters in Rostov-on-Don “did not do anything reprehensible” and had simply “followed the orders of their command.”

“They didn’t offend anyone, they didn’t break anything,” he said. “No one has the slightest claim against them — neither the residents of Rostov, nor the military personnel of the Southern Military District, nor the law enforcement agencies.”