Larossi Abballa, who killed a police commander and his partner, said Euro 2016 "will be like a cemetery," a police source told CNN.
On Tuesday, Russia was handed a suspended ban from Euro 2016 and could still be thrown out of the tournament if there is more trouble from its traveling fans.
European football's governing body, UEFA, meted out the punishment after scenes of disturbance marred Russia's opening match against England in Marseille on Saturday.
Dozens of fans were injured in clashes outside the Stade Velodrome
in the French port city, while Russia fans were charged with "crowd disturbances, use of fireworks and racist behavior" inside the stadium.
UEFA warned Russia could be disqualified if there is a repeat of crowd trouble inside grounds where the team is playing.
"This decision only relates to the incidents which occurred inside the stadium and are therefore the jurisdiction of the UEFA Disciplinary Bodies," the UEFA statement
Russia coach Leonid Slutsky and forward Artem Dzyuba said Tuesday they are "convinced" that the suspended disqualification
will not go into effect.
"What's happened is unacceptable," commented Dzyuba on the fans' behavior. "We don't support anyone hitting anyone. Above all, let us focus on football."
Russia was also fined €150,000 ($168,000).
The team's supporters will be under scrutiny when Russia faces Slovakia in Lille on Wednesday, although UEFA has made it clear it will only dole out further punishment for any incidents which take play inside the tournament's stadiums.
There were disturbing acts of violence between Russia and England fans
on the streets of Marseille on Saturday.
In chaotic scenes involving hundreds of fans, throngs of rival supporters rushed at one another, hurling bottles, chairs and other objects, and forcing police in riot gear to fire tear gas in response.
Footage emerged of men kicking and stomping on another person lying on the street, as the rivalry turned violent prior to kickoff.
Then, at the end of the game, Russian fans charged at the section of the stadium containing England supporters, and more chaos ensued. Smoke filled the streets as panicked fans fled.
At least 35 people were injured, four of them seriously, said Mathieu Duroselle, a spokesman for Marseille police. The number included three officers who suffered slight injuries, he said.
Eight people were arrested, including British, Russian and French citizens.
UEFA confirmed that England has not been sanctioned for its fans' behavior inside the stadium, but five England supporters were given jail sentences
for throwing bottles in outside clashes.
The focus of attention now turns to Lille, where Russia and England fans are gathering ahead of the next group matches. England is playing British rival Wales in nearby Lens, which is 30 minutes by train from Lille.
The English Football Association (FA) has already questioned the adequacy of security arrangements in Lille.
"We have serious concerns around the security arrangements for the city in the next few days," its chairman Greg Dyke said in a statement on Monday.
"These concerns are heightened with the knowledge that Russia will play in Lille on Wednesday afternoon.
"We know that UK police authorities are stepping up their support on the ground, but we would urge you to bring the policing authorities in both Lille and Lens together as soon as possible to ensure there is a coordinated and effective plan in place."
Dyke added that more could have been done to prevent the troubling scenes inside the Marseille stadium during England's 1-1 draw with Russia.
"We believe the stewarding arrangements in place (in Marseille) were unacceptable. Supporters were able to get in with fireworks and flares, and then let them off, and there was insufficient segregation between the Russian and English fans."
The UK Government is deploying additional police, specifically trained in football disorder, to France ahead of the match against Wales.
Fabienne Buccio, prefect of the Pas-de-Calais region, added Lens will be "in lock down by the police." More than 1,200 officers are expected to patrol the streets, plus another 1,200 private security staff.
France remains in a state of high alert following the ISIS Paris terrorist attacks in November 2015, which killed 130 people.
The country suffered another terror attack Monday
when a French police commander and his partner were killed in a knife attack in Magnanville, northwest of Paris.
U.S. and British officials have both warned citizens about the potential terror risk of attending Euro 2016 games.