President Vladimir Putin decries "betrayal" and "treason" following a dramatic challenge by the chief of the Wagner mercenary force.
Yevgeny Prigozhin called for a rebellion against the army - although he has denied attempting a coup.
Without mentioning Prigozhin by name, Putin vowed to punish those behind the armed mutiny.
He acknowledged that the situation in the southern city of Rostov-on-Don, taken by Wagner, remained difficult.
Wagner says it controls the city near the Ukraine border, where residents have been told to stay indoors.
On Friday night, security in Russia was tightened, the internet was restricted and military trucks were spotted on Moscow street.
Prigozhin accused the army of launching a deadly attack on his forces in Ukraine, where Wagner troops are fighting for Russia - Moscow denies this
In a message posted to Telegram on Saturday morning, Yevgeny Prigozhin said that all the members of his Wagner group of mercenaries were "ready to die" in his action against the Russian military.
"All of us are ready to die. All 25,000, and then another 25,000," he said in an audio message, adding the action was being taken "for the Russian people".
