Earlier, the group's chief said he had told his fighters to return to Ukraine to avoid bloodshed.

Yevgeny Prigozhin will now move to neighbouring Belarus and charges against him and his troops will be dropped, Russian state media reports.

It signals the end of a chaotic and extraordinary day in Russia.

The Wagner Group is a private army of mercenaries that has been fighting alongside the regular Russian army in Ukraine.

Tension had been growing between them over how the war has been fought, with Prigozhin launching vocal criticisms of Russia's military leadership in recent months.

It came to a head on Saturday morning, when Wagner mercenaries crossed the border from their field camps in Ukraine and entered the southern city of Rostov-on-Don.

In developments that were breathlessly fast, they reportedly took over the regional military command and seized military facilities in Voronezh, another city further north, towards Moscow.

The fighters started to march toward the capital, prompting the Kremlin to introduced tighter security in many regions, including Moscow, where the mayor of the capital city had told residents to avoid travelling.

There were also warnings that thousands of elite Chechen troops were heading to Moscow to fight off the Wagner soldiers, if needed.

In response, President Vladimir Putin had pledged to punish those who had "betrayed" Russia.

The agreement to suddenly de-escalate the situation came on Saturday evening, after Belarusian leader Alexander Lukashenko held talks with Prigozhin, according to Russian TV channel Rossiya 24.

Hours later, video emerged purportedly showing Wagner troops leaving Rostov, and their leader being driven away to the cheers and handshakes of supporters.

Commenting on the day's events, Ukraine's President, Volodymyr Zelensky said the situation was "complete chaos".

"The man from the Kremlin is obviously very afraid and probably hiding somewhere, not showing himself. I am sure that he is no longer in Moscow," he said in a statement.

"He knows what he is afraid of, because he himself created this threat. All evil, all losses, all hatred - it is he who spreads it."

There were rumours that Mr Putin had fled Moscow, after flight tracking showed that two presidential planes had left the city on Saturday.

However his press secretary, Dmitry Peskov, said the president was still in the Kremlin.

Mr Peskov added that the arrest warrant for Prigozhin would be dropped and criminal case against him and his troops would be closed.

Wagner mercenaries who wish to sign a contract with the Russian Ministry of Defence can still do so, the press secretary said.