Putin urges Wagner members Monday to sign contract with Russia's defense ministry, return home or go to Belarus.
The criminal case against Prigozhin has not been closed, Sputnik reported, citing a source in the Russian Prosecutor General's Office.
Wagner mercenary group halts advance on Moscow Saturday in a deal brokered by Belarusian president.
Wagner forces had reached the city of Lipetsk, some 450 kilometers south of Moscow.
The Kremlin dismissed a US media report on Wednesday suggesting a top Russian general had known in advance about an aborted mutiny last week by the Wagner private military group, calling it "speculation and gossip".
Kremlin spokesman Dmitry Peskov was responding to a question regarding a New York Times report citing United States officials as saying that General Sergey Surovikin, deputy commander of Russia's military operations in Ukraine, had advance direct knowledge of the planned mutiny.
Belarusian President Alexander Lukashenko confirmed on Tuesday that Yevgeny Prigozhin, head of the Wagner private military group, had arrived in Minsk, as NATO warned it was ready to defend against "Moscow or Minsk".
Russian Defense Minister Sergei Shoigu has appeared on state media inspecting Russian troops in Ukraine, making his first public appearance following an armed rebellion by the Wagner private military group.
MOSCOW - The legal regime of the counter-terrorist operation against the Wagner private military group has been canceled in Moscow and the Moscow region due to the normalization of the current situation, said the Russian government.
"Due to the absence of threats to life, health, property and other legally protected interests of people, the head of the counter-terrorist operation, the head of the Federal Security Service of Russia for the city of Moscow and the Moscow region decided to cancel the counter-terrorist operation legal regime in Moscow and the Moscow region from 09:00 a.m. local time (1200 GMT) on Monday," said Russia's National Anti-terrorism Committee in a statement.
Editor's note: Moscow and Yevgeny Prigozhin, head of the Wagner group, arrived at a compromise thanks to mediation by Belarusian President Alexander Lukashenko late on Saturday. Two experts talk to China Daily's Zhang Xi and Pan Yixuan about the impact of the incident.
China expressed its support for Russia's efforts in maintaining its stability, a Foreign Ministry spokesperson said on Sunday, a day after a rebellion by a Russian mercenary force was resolved peacefully.
How is life in Moscow unfolding after the recent incident involving the Wagner group? Join Ren Qi, a China Daily reporter based in Russia, as he takes you to the city center near Red Square to provide you with the latest updates.
MOSCOW -- Moscow and Yevgeny Prigozhin, head of the Wagner private military group, reached a compromise through the mediation of Belarusian President Alexander Lukashenko late Saturday,according to RIA Novosti news agency reports.
Russian President Vladimir Putin said in a national address on Saturday that an "armed mutiny" by the Wagner militia group was treason, and that anyone who had taken up arms against the Russian military would be punished.
Russia's FSB security service has opened a criminal case against Yevgeny Prigozhin, head of Russia's Wagner private military group, for calling for armed mutiny, Russian media reported on Friday, citing the National Antiterrorism Committee.
Suspect detained for St. Petersburg blast while Kremlin accuses West of hypocrisy
Ukrainian President Volodymyr Zelensky's party said on Sunday that it would move to replace its defense minister, as Russian forces close in on Bakhmut amid heavy fighting.
One of Russian President Vladimir Putin's closest aides said on Tuesday that Moscow was now fighting the US-led NATO military alliance in Ukraine and that the West was trying to wipe Russia from the political map of the world.
BRUSSELS - The European Union (EU) Monday adopted sanctions against the Russian paramilitary group Wagner, amid its concerns of the alleged Russian military build-up along the eastern Ukraine borders.