In the first public remarks released since he was last seen on Saturday night, Wagner Group chief Yevgeny Prigozhin said his fighters had halted their campaign to avert bloodshed.
"We went as a demonstration of protest, not to overthrow the government of the country," Prigozhin said in an 11-minute audio message released on the Telegram messaging app.
"Our march showed many things we discussed earlier: the serious problems with security in the country."
He said his goal had been to prevent his Wagner militia's destruction, and to force accountability on commanders who had botched Russia's military campaign in Ukraine. He said his fighters did not engage in combat on the ground in Russia, and regretted having to shoot down Russian aircraft that had fired on them.
The armed mutiny over the weekend by the powerful mercenary outfit and its abrupt ending with no apparent penalties for the perpetrators or their leader were followed on Monday by other official moves to return the country to normal.
Russia's national Anti-Terrorism Committee said the situation in the country was stable, and Moscow Mayor Sergei Sobyanin said he was cancelling a counter-terrorism regime imposed in the capital Moscow.
Monday had been declared a non-working day in Moscow to allow time for things to settle.
A former Putin ally and ex-convict whose forces have fought the bloodiest battles of the 16-month war in Ukraine, Prigozhin, 62, this month defied orders to place his troops under Defense Ministry command.
He launched the rebellion on Friday after alleging the military had killed some of his men in an air strike which the Russian defence ministry denied.
Prigozhin was last seen heading north from Rostov-on-Don in an SUV, smiling as his men exchanged fist bumps with passers by before pulling out.
Negotiations took place while the armed column was moving toward Moscow. Reports say Prigohzin was offered amnesty if he moved to Belarus, but his presence there has not been confirmed.
The Kremlin said the question of General Staff personnel changes, as Prigohzin demanded, was the sole prerogative of the president and could hardly have been part of any deal.
The developments were, at face value, one of the biggest challenges to his rule after more than two decades in power.
"Saturday was a very emotional and tense day," Russia's ministry of digital affairs said, recommending that IT, telecoms and media companies give employees the day off on Monday.
Russian intelligence services were investigating whether Western spy agencies played a role in the aborted mutiny, the TASS news agency quoted Foreign Minister Sergei Lavrov as saying on Monday.
Meanwhile, the U.S. intelligence community "was aware" that the mutiny orchestrated by Wagner chief Yevgeny Prigozhin's mutiny "was a possibility" and briefed Congress "accordingly" before it began, said a source familiar with the issue, who spoke on condition of anonymity.
President Joe Biden said he had directed his national security team to update him on the situation "hour by hour" and to prepare for a range of scenarios, which he did not detail.
U.S. Secretary of State Antony Blinken suggested the turmoil could take months to play out.
"We've seen more cracks emerge in the Russian facade," Blinken told NBC's "Meet the Press" program on Sunday.
His perspective was echoed by German Foreign Minister Annalena Baerbock, who said "We are seeing massive cracks in the Russian propaganda"before heading into an EU meeting..
She said Putin's war in Ukraine, which he calls a "special military operation" to counter a threat from there and the West to Russia and Russians, was destroying Russia and that Western allies would continue to back Ukraine.
Meanwhile, Ukraine says its forces have reclaimed some 130 square km along the southern front line since the beginning of their counteroffensive earlier this month.
Deputy Defense Minister Hanna Maliar told state television on Monday there had been little significant change in the past week and Russia denied Ukrainian reports of small advances around the battleground city of Bakhmut.
Serhiy Nayev, commander of Ukraine's Joint Forces, responded to speculative reports that Wagner fighters - reported at the weekend to be heading back to Russian-held areas of Ukraine - could be moved to Belarus to attack Ukraine from the north.
"If this happens and the enemy tries to cross the state border, it will be nothing but suicide for them,” Nayev said on Telegram.
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