England manager Roy Hodgson and captain Wayne Rooney have appealed directly to fans to avoid repeats of the violence that has marred the start of Euro 2016.
French prosecutors said 150 Russians were behind the most serious clashes before Saturday's 1-1 draw between the two countries in Marseille.
But both teams now face expulsion from Uefa if there is any further violence.
"I am very concerned at the threat now hanging over us," said Hodgson.
"We have worked very hard to get here and desperately want to stay.
"We appreciate all your support at the matches, of course, but I am appealing to you to stay out of trouble and to try to make certain these threats being issued are never carried out and we will be able to attempt to do the best we can to stay in this competition by football means."
Manchester United forward Rooney asked fans to be "safe and sensible", but not to travel to France without tickets.