Russian President Vladimir Putin has offered a choice to Wagner mercenaries who took part in the weekend’s armed rebellion in his first address to the nation since the revolt.

Mr Putin said on Tuesday morning (AEST) that Wagner fighters who “did not shed blood” would be allowed to sign a contract with the Russian military, return to their families or move to Belarus.

In a five-minute video, Mr Putin said the “armed rebellion would have been suppressed anyway” as the plotters “realised their actions were criminal”.

The man who led the aborted mutiny, Wagner boss Yevgeny Prigozhin, also broke his silence, saying he never intended to topple Russia’s government.

In an 11-minute audio released Tuesday morning (AEST), Mr Prigozhin insisted the troop advance on Moscow was a “march for justice”.

“We went as a demonstration of protest, not to overthrow the government of the country,” Mr Prigozhin said in the message released on the Telegram messaging app.

“Our march showed many things we discussed earlier: the serious problems with security in the country.”

Mr Prigozhin gave few clues about his own fate and whereabouts or the deal under which he stood down.

He has not been seen since Saturday night (local time) when he was smiling and high-fiving bystanders from the back of an SUV as he withdrew from a city occupied by his men.

Also on Tuesday, US President Joe Biden “made it clear” the US was not involved and was watching closely to see what would transpire.

“We made sure we gave Putin no excuse to blame this on the West and to blame this on NATO,” he said.

“We were not involved. We had nothing to do with it, this was part of a struggle within the Russian system.”

Mr Biden said: “It’s still too early to reach a definitive conclusion about where this is going.”

Wagner chief speaks

Mr Prigozhin 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.

In another dig at those commanders, Mr Prigozhin said his private army’s nearly 1000-kilometre march to the capital on Saturday went better than the invasion of Ukraine.

He said if his troops had carried out the “special military operation” in Ukraine, it would have been over much sooner.

Mr Prigozhin 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.

“We halted at the moment when the first assault unit deployed its artillery [near Moscow], conducted reconnaissance and realised that a lot of blood would be spilled.”

Mr Prigozhin renewed an allegation that the Russian military had attacked a Wagner camp with missiles and then helicopters, killing about 30 of its men. He said this had been the immediate trigger for what he called a “march of justice”.

He made no mention of his own whereabouts or future plans, and revealed no further details of the mysterious agreement that brought a halt to his mutiny.

On Saturday he had said he was leaving for Belarus under a deal brokered by that country’s president.

Mr Prigozhin shocked the world by leading Saturday’s armed revolt, only to abruptly call it off as his fighters approached the capital having shot down several aircraft but meeting no resistance on the ground.

Russia’s three main news agencies reported on Monday that a criminal case against Mr Prigozhin had not been closed, an apparent reversal of an offer of immunity publicised as part of the deal that persuaded him to stand down.

Mikhail Mishustin, who leads Mr Putin’s cabinet as his appointed prime minister, acknowledged that Russia had faced “a challenge to its stability” and called for public loyalty.

“We need to act together, as one team, and maintain the unity of all forces, rallying around the president,” he told a televised government meeting.

Authorities also released video showing Defence Minister Sergei Shoigu flying in a plane and being briefed, also containing no evidence of when it was filmed.

One of Mr Prigozhin’s principal demands had been that Mr Shoigu be sacked, along with Russia’s top general, who by Monday night had yet to appear in public since the mutiny.

Moscow mayor Sergei Sobyanin, who had told residents to stay indoors on Saturday as the mutinous fighters raced to within a few hundred kilometres of the capital, said he was cancelling a counter-terrorism security regime.

Foreign Minister Sergei Lavrov said Russia’s intelligence services were investigating whether foreign spy agencies played a role in the aborted mutiny, the TASS news agency reported.

Mr Prigozhin, 62, a former Putin ally and ex-convict whose forces have fought the bloodiest battles of the 16-month war in Ukraine, defied orders this month to place his troops under Defence Ministry command.

He complained on Monday about a military order that all volunteer units including Wagner are meant to sign by July 1 placing themselves under the control of Russia’s Defence Ministry.

-with AAP