Russia will be thrown out of Euro 2016 if their fans cause further trouble, says European governing body Uefa.
The Russians have also been fined 150,000 euro (£119,000) following violent scenes at the game against England in Marseille on Saturday.
The suspended disqualification and fine relate only to incidents that happened inside the stadium.
Meanwhile, groups of Russian fans are also being deported from France as a result of trouble at the tournament.
A French police operation to arrest 40 suspected Russian hooligans is under way.
Russia coach Leonid Slutsky, whose team still have to play Wales and Slovakia, is confident his squad will not be excluded.
"We are sure our supporters will not do the same and will not give any reasons to disqualify our team," he said.
Russia forwards Artem Dzyuba added: "We're not at a streetfighting championship. Please, let's focus on football."
England were also threatened with disqualification from Euro 2016 but were not formally charged by Uefa.