Russia's Defence Ministry said in a statement addressed to Wagner Group mercenary fighters on Saturday that they had been "deceived and dragged into a criminal adventure" by Wagner chief Yevgeny Prigozhin.
In a statement posted on Telegram, the ministry urged Wagner fighters to contact its representatives and those of law enforcement services, and promised to guarantee their security.
In a statement, the country's Defense Ministry said Wagner chief Yevgeny Prigozhin tricked the fighters into "criminal adventure" and "armed rebellion" as the Kremlin gave orders for his arrest over inciting mutiny.
"We appeal to the fighters of the assault squads 'PMC Wagner.' You were tricked into Prigozhin's criminal adventure and participation in an armed rebellion," the statement said.
The Russian side further said many Wagner fighters had "realized their mistake" and were asking for help to return to their bases.
"Please be prudent and get in touch with representatives of the Russian Ministry of Defense or law enforcement agencies as soon as possible. We guarantee everyone's safety," it added.
Prigozhin said early Saturday that his forces in Ukraine have crossed into the Russian city of Rostov.
Tensions between the Kremlin and Wagner escalated after Prigozhin accused Russian forces of attacking his mercenaries.
Russia denied those claims late Friday and issued arrest orders for Prigozhin.
Prigozhin has, in recent months, repeatedly accused the Russian Defense Ministry and Defense Minister Sergey Shoygu of not supplying sufficient arms to the paramilitary group.