European soccer's governing body warned the English and Russian soccer associations on Sunday their teams could be disqualified from Euro 2016 if there was more of the fan violence that has injured several dozen people.
UEFA's threat came after it began disciplinary proceedings against the Russian federation on Sunday following ugly scenes inside Marseille's Stade Velodrome stadium at the end of Saturday's match between England and Russia.
Masked Russian fans charged at England supporters, punching and kicking them. Some England fans had to scramble over barriers to escape.
UEFA said it would also investigate allegations of racist behaviour and the throwing of missiles and fireworks.
The violence in the stadium followed three days of clashes between English, Russian and French fans in the Mediterranean port city of Marseille that drew a strong response from riot police.
UEFA said it was "disgusted" and would not hesitate to impose sanctions, including "the potential disqualification of their respective teams from the tournament, should such violence occur again". It said a decision on sanctions against Russia would be made on Tuesday.
French Interior Minister Bernard Cazeneuve called the fans' behaviour barbaric and said it was "absolutely necessary that national federations whose supporters create incidents of this nature be penalised".
A ministry spokesman said Cazeneuve was not calling for Russia and England to be punished, but rather supporting UEFA's stance.
The minister also said he had asked the cities hosting Euro 2016 fixtures to ban the sale and consumption of alcohol in zones where the risk of confrontation was most acute.
English and Russian fans will almost certainly cross paths in northern France later this week, with Russia playing Slovakia in Lille on Wednesday and England facing Wales only 40 km (25 miles) away in Lens on Thursday.
Russian Sports Minister Vitaly Mutko, who had initially denied there had been any crowd disturbance, said UEFA was right to investigate.
It is the second time in as many European Championship tournaments that the Russian federation has faced sanctions because of its fans.
Russia was fined and given a suspended six-point deduction for its Euro 2016 qualifying campaign after fans assaulted stadium security staff and displayed illicit banners at the 2012 tournament in Poland and Ukraine.
The British government urged calm on all sides and offered to send more police to France ahead of England's next game.
Violence also briefly erupted in Nice, where Northern Irish and local fans hurled glass bottles and chairs at each other late on Saturday.
Police said they had arrested 15 people after scuffles ahead of Sunday's game between Turkey and Croatia in Paris.
The French government rallied behind the police amid questions over tactics and security inside the stadiums.
"SOCCER IS SICK"
"If there is a failure, it is that of soccer, which is sick because some of its fans drink excessively and fight," Interior Ministry spokesman Pierre-Henri Brandet said on BFM-TV.
A UEFA spokesman said more security personnel would be deployed to segregate rival fans inside stadiums.
The tournament is being played under a state of emergency after Islamist militants attacked Paris in November, killing 130 people.
Further questions over security were raised when flares and a smoke bomb were let off at the Parc des Princes in Paris during Turkey's match against Croatia on Sunday. UEFA said it would not comment before it received the referee's match report.
In Marseille, some English fans suggested French riot police had been heavy-handed and quick to fire tear gas. Thirty-five people were hurt in the fighting, including one English fan who suffered a heart attack.
Marseille police chief Laurent Nunez told France Info radio his force's response prevented "much more serious damage". Fifteen people, mostly English, were arrested in the city over three days.
In 2000 UEFA threatened to kick England out of the tournament after violence broke out between English and German fans in the Belgian cities of Brussels and Charleroi.
France has enlisted more than 90,000 police, soldiers and private security agents nationwide to ensure safety in the face of intelligence agency warnings of potential militant attacks and the threat of hooliganism.