Putin-ally Prigozhin leads a mercenary force of thousands, including ex-convicts, in the Ukraine war.
According to a statement on Telegram, Prigozhin, an ally of Russian President Vladimir Putin, is accused of the “encroachment on the territorial integrity and inviolability of Ukraine” and “waging an aggressive war”.
The statement said fighters who fled the group “will not avoid responsibility”.
“Prosecutors have already interrogated two such fighters who are in the EU. An investigation into the involvement in war crimes of another PMK member, who is in Norway under way,” the statement said.
Norwegian police are currently interrogating former Wagner group commander Andrey Medvedev, who fled from Russia to Norway last month after fighting in Ukraine.
Earlier this week, Medvedev told the Reuters news agency that he was speaking out against the Wagner group to ensure perpetrators were brought to justice.
“Medvedev gives the impression that he wants to continue to say more” about his time with Wagner, the police have said.
Security arrangements have also been made for Medvedev’s safety, “both visible and non-visible” measures, they added, without giving specifics.
Another former Wagner fighter, Marat Gabidullin, is understood to be seeking asylum in France.
The previously shadowy group has taken centre stage during the invasion of Ukraine and is associated with the bloody battle for Bakhmut in the east of the country.
Late in January, the United States designated Russia’s Wagner mercenary group as a “transnational criminal organisation”, piling pressure on the private army that has recruited tens of thousands of Russian prisoners to fight in Ukraine.