Russian President Vladimir Putin thanked Wagner commanders and soldiers who avoided bloodshed, saying most of them are patriots.

Putin said he would honor his promise to allow Wagner fighters to relocate to Belarus if they wanted, or to sign a contract with the Defense Ministry or simply return to their families.

He made no mention of mercenary chief Yevgeny Prigozhin, who led the mutiny.

He also said that he gave the order to avoid bloodshed during an armed rebellion over the weekend that rattled his rule, saying the West and Kyiv wanted Russians to "kill each other" and thanking citizens for their "patriotism."

"From the start of the events, on my orders steps were taken to avoid large-scale bloodshed," Putin said in a televised address, thanking Russians for their "endurance and unity, and patriotism".

"It was precisely this fratricide that Russia's enemies wanted: both the neo-Nazis in Kyiv and their Western patrons, and all sorts of national traitors. They wanted Russian soldiers to kill each other," he said.

If mercenaries and regular troops had fired at each other, only Kyiv and the West would have benefited, but Russian society had proven to be united in its rejection of the uprising, he said.

"The armed mutiny would have been suppressed in any case. The mutiny's organizers, despite their loss of judgment, could not but understand this," he said.

He also thanked Belarusian strongman Alexander Lukashenko for mediating with Wagner boss Yevgeny Prigozhin, who is now thought to be in Belarus after calling off the group's advance on Moscow, but his whereabouts have yet to be confirmed.

Putin, who did not mention Prigozhin by name, offered Wagner fighters the option of serving with the Russian military.

All attempts to sow chaos in Russia were destined to fail, he said. "The organizers of the mutiny, who betrayed the country, also betrayed those who were on their side," he said.

In his first comments after the failed uprising, Prigozhin denied seeking a change of power in Moscow.

"We went out to demonstrate, not to overthrow the authorities in the country," the 62-year-old said in a voice message circulated by his press service on Telegram on Monday.

Prigozhin did not give details of his current whereabouts.

He repeated his accusation that the Russian Ministry of Defence shelled the military camps of his mercenaries on Friday.

According to Prigozhin, 30 Wagner fighters were killed, which in addition to what he said was the ministry's aim of dissolving Wagner and transferring the personnel to the regular army, was the trigger for the march towards Moscow.

Prigozhin, long considered a close ally of Putin but labeled a traitor after the weekend's uprising, acknowledged that the protest had claimed lives.

"During our march, not a single soldier was killed on the ground. We regret that we were forced to shoot down flying objects, but that is because they bombed us," he said.

According to reports by Russian military bloggers, six Russian army helicopters and one aircraft were destroyed and their crews were killed in the clash. Officially, the Russian leadership has not acknowledged these losses.

Prigozhin, in turn, praised the march on Moscow as exemplary of how the full-scale invasion of Ukraine ordered by Putin on February 24, 2022, should have proceeded.

A rapid advance of units, the elimination of all military sites of the enemy on the way - and practically without casualties. On the Wagner side, two soldiers were killed and several mercenaries were injured, Prigozhin said.

U.S. President Joe Biden said he was watching events and denied claims Washington was involved in the uprising: "We're going to keep assessing the fallout of this weekend's events and the implications for Russia and Ukraine."

"We made clear that we were not involved. We had nothing to do with it. This was part of a struggle within the Russian system."

"The ultimate outcome of all this remains to be seen," Biden said on Monday.

Criminal proceedings against Prigozhin have not yet been dropped, according to media reports from Moscow on Monday.

Investigators from Russia's FSB domestic secret service continue to investigate the case, the daily Kommersant reported, citing the investigators.

"Investigations are ongoing," the Russian news agency Interfax also reported, citing its own unspecified source.

The Kremlin announced on Saturday evening that criminal proceedings against Prigozhin and the Wagner insurgents would be dropped.

In a speech on Saturday, Putin said that the masterminds behind the uprising would face their "inevitable punishment."

The announcement that followed later, indicating that the rebels would go unpunished after the end of the revolt, caused astonishment across the country. Commentators interpreted Putin's concession as a weakness.

According to local media, Wagner offices have been raided in St Petersburg, where Prigozhin has been based until now.

Advertising posters used by the private army to recruit volunteers for military service in Ukraine have also been removed throughout Russia.

Thousands of mercenaries serve in the Wagner force. The social network VK - the Russian counterpart of Facebook - blocked Wagner's page on the instructions of the prosecutor general's office.

Lukashenko and Prigozhin, who, according to the Kremlin, have known each other for about 20 years, had independently stated that the withdrawal of the Wagner troops was intended to prevent "bloodshed" in Russia.

Prigozhin had leveled serious accusations against Defence Minister Sergei Shoigu and Chief of General Staff Valery Gerasimov, citing their alleged military misconduct as the reason why he wanted his fighters to oust them.

After Prigozhin surprisingly declared his uprising to be over on Saturday evening, speculation increased as to whether there might now be personnel changes in the Russian military leadership.

On Monday the state of emergency imposed in Moscow following the attempted uprising was lifted.

The anti-terror emergency was also lifted in the greater Moscow region and in the Voronezh region further south.