Paris - UEFA on Sunday threatened to kick Russia and England out of the European Championship finals if their fans are involved in more violence.
The threat followed three days of violence in Marseille, culminating in pitched battles between Russian and English supporters before Saturday's match between the countries.
Dozens of people were injured after the worst violence at an international tournament since the 1998 World Cup.
Russian fans also charged into an English section of the Stade Velodrome at the end of the 1-1 draw and sparked fighting.
With more high-risk matches to come, the UEFA executive committee made a public "warning" in a statement which expressed "disgust" for the clashes.
A UEFA inquiry into the Marseille trouble will recommend punishment on Tuesday.
The executive committee said "it will not hesitate to impose additional sanctions on the Football Association (FA) and the Russian Football Union (RFU), including the potential disqualification of their respective teams from the tournament, should such violence occur again."
World body FIFA also condemned what it called the "shameful scenes" between "idiotic troublemakers".
Russia was charged with crowd disturbances, racist behaviour and letting off fireworks for its fans' part in the stadium trouble. But UEFA also said mistakes were made segregating the rival supporters.
Authorities are now on red alert for Russia's next game in Lille, northern France, on Wednesday against Slovakia.
England's next Group B game against Wales in nearby Lens on Thursday has already been classed as a high-risk game by the French authorities.
More British police
The British government said it was "deeply concerned" by the violence in Marseille and offered to send more police to France.
It was looking into "reports that in some cases England fans were attacked by rival supporters," a spokesman said.
"We have offered to send further UK police to France ahead of the next England game to support the security operation around the match in Lens."
Russia's Sports Minister Vitaly Mutko said his country's fans "behaved improperly" and conceded UEFA was likely to impose a fine. But he laid the blame on the match organisers for failing to separate supporters.
Turkey's match against Croatia in Paris on Sunday was also classified as high-risk but there was no major trouble.
There were brief scuffles when around 50 French youths threw bottles at Croatian fans, but they were quickly dispersed by police before the match which ended in a 1-0 win for Croatia.
Authorities in Marseille said three people remained in hospital in a "serious" state on Sunday following the clashes.
They included an England supporter who had initially been fighting for his life after apparently being beaten on the head with an iron bar.
Hundreds of fans who has been drinking heavily pelted each other with cafe chairs and bottles in the Vieux-Port area of Marseille. Witnesses said French youths were also involved.
More than 1,200 riot police fought to control the crowd with teargas and 10 people, including Russians, French, German and Austrian nationals were arrested.
English fans said the clashes had been caused by Russian supporters, who charged them.
"There were about 100 Russians. They just came out of nowhere, something was thrown and that started it all off," said one England supporter, who asked not to be named.
The scenes in Marseille were reminiscent of incidents in the same city during the 1998 World Cup, when English and Tunisian fans were involved in a mass brawl.
Later Saturday, the violence spread along the Mediterranean coast to Nice, where Northern Ireland fans were drawn into fights with local youths and seven people were hurt, witnesses and police said.
In Lyon, four French men aged between 20 and 24 were briefly detained following a fight in a bar where England fans had been drinking, police said.
The violence has raised concerns about Russia's hosting of the 2018 World Cup.
'Back in dark ages?'
The scenes in Marseille caused anger in England, which had hoped it had thrown off its past reputation for football hooliganism.
"Back in the dark ages?" said The Mail on Sunday newspaper while the Sunday Telegraph said the rioting fans were a "disgrace".
The violence has marred the start of the tournament after the buildup was overshadowed by months of industrial unrest and fears of jihadist attacks.
The strikes in protest at the government's labour market reforms are set to go on this week. Action by a quarter of the Air France's pilots will ground 20 percent of flights on Monday, the airline said..
The strike is set to continue until Tuesday, when unions have organised nationwide rallies to protest government labour reforms.