A Russian criminal case against mercenary leader Yevgeny Prigozhin for mutiny remains open and is still being investigated, the Kommersant newspaper and Russia's three main news agencies reported on Monday, citing unidentified sources.

President Vladimir Putin on Saturday vowed to crush what he called a treasonous mutiny after Prigozhin said his Wagner Group fighters had taken control of the southern city of Rostov and were heading to Moscow on what he said was a "march for justice" intended to remove corrupt and incompetent Russian commanders.

Under a deal mediated by Belarusian leader Alexander Lukashenko that defused the crisis late on Saturday, the Kremlin said a criminal case against Prigozhin would be dropped and he would move to Belarus. His fighters would return to base and would also face no legal action, the Kremlin said.

However, Russia's Kommersant newspaper reported on Monday that the criminal case remained open and that the Federal Security Service (FSB) was continuing its investigation as part of the case. It cited an unidentified source as saying there had not been enough time to close the case.

Russia's three main news agencies – TASS, RIA and Interfax – also reported that the criminal case against Prigozhin remained open and that the investigation was continuing.

"The criminal case against Prigozhin has not stopped," TASS cited a source close to the prosecutor's office as saying. "The investigation is ongoing."

The prison term under Russian law for such a crime is 12-20 years.

Prigozhin, who has not been seen in public since leaving Rostov late on Saturday and has not commented on the deal, denied leading a mutiny. Once a close Putin ally whose Wagner Group has spearheaded much of the fighting in Ukraine, Prigozhin launched his rebellion on Friday after alleging that the Russian military had killed some of his men in an air strike.

The Defence Ministry denied his claim.

Meanwhile, Russian Defence Minister Sergei Shoigu was shown speaking to troops in a video released by his ministry on Monday, his first known appearance in public since the mutiny by the Wagner Group.

There was no sound on the video and it was not immediately clear where or when the visit had taken place.

Shoigu was shown flying in a plane with a colleague and hearing reports at a command post run by Russia's Zapad (West) military grouping.

The Defence Ministry TV channel, Zvezda, said Shoigu, who looked physically unharmed and calm, had listened to a report by Colonel General Yevgeny Nikiforov, the group's commander, about the current situation on the front lines in Ukraine.

In his mutiny during which he seized control of Russia's military headquarters in southern Russia, Prigozhin had demanded that Shoigu and Valery Gerasimov, the Chief of the General Staff, be handed over to him so that he could "restore justice".

Prigozhin accused both men of gross incompetence and corruption and had long been agitating for their removal.

Gerasimov has not been seen since in public, and there was no word from the Kremlin about any new personnel changes when it described the deal that had ended the mutiny. (Reuters)