With the tournament facing new high risk games, French authorities said three people remained in serious condition in hospital in Marseille after the clashes before and during Saturday’s game.
European football’s governing body said Russian fans faced accusations of crowd disturbances, racist behaviour and setting off flares at the Stade Velodrome.
In chaotic scenes, Russian supporters appeared to charge into the English supporters’ section of the stadium after the 1-1 draw and fists were thrown.
The disturbances followed a day of pitched battles between fans in the centre of Marseille in the worst violence at an international tournament since the 1998 World Cup.
One of the seriously injured was an England supporter who had initially been fighting for his life after apparently being hit on the head with an iron bar.
More than 30 other people had minor injuries.
Fears of new violence ran high as Turkey prepared to face Croatia in Paris in a match on Sunday which organisers have also identified as high-risk.
“UEFA expresses its utter disgust for the violent clashes that occurred in the city centre of Marseille, and its serious concern for the incidents at the end of the match inside Stade Velodrome,” it said.
“This kind of behaviour is totally unacceptable and has no place in football.”
UEFA said there were “issues” with the segregation at the stadium and it would strengthen the deployment of security personnel at future matches.
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.
The violence in the stadium was limited compared to the scenes before the match when hundreds of fans who has been drinking heavily pelted each other with cafe chairs and bottles in the Vieux-Port area of Marseille.
More than 1,200 riot police fought to control the crowd with teargas.
Ten people, including Russians, French, German and Austrian nationals were arrested, police said.
English fans said the clashes had been caused by Russian supporters, who charged at 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, witnesses said.
Seven people were injured there including one man who suffered a serious head injury, 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.
‘High-risk’ Croatia match
In a game also seen as “high-risk” by organisers, Turkey and Croatia will play at Paris’ Parc des Princes stadium at 1300 GMT.
Croatian fans also have a history of violence at football matches and more than 1,500 police will be on duty.
Police will also be heavily deployed at Thursday’s Germany-Poland game in Paris, and England’s next match against Wales in Lens in on Thursday.
Authorities are also concerned about the Ukraine-Poland match in Marseille on June 21.
The violence has raised concerns about Russia’s hosting of the 2018 World Cup.
“Of course as hosts of the future World Cup we need to preserve our image and people shouldn’t spoil it. That’s the worst thing,” Sports Minister Mutko said.
The scenes in Marseille caused revulsion in England, which had hoped it had thrown off its past reputation for football hooliganism.
“What is wrong with these people? An absolute embarrassment to the country,” tweeted former England striker Gary Lineker.
“Back in the dark ages?” said The Mail on Sunday newspaper.
The Sunday Telegraph said the rioting fans were a “disgrace” while French sports daily L’Equipe said: “Fear has already won at the Euros.”
The violence has marred the start of the tournament after the buildup was overshadowed by months of industrial unrest and fears of a repeat of the Paris attacks on November 13.
The strikes in France have showed little sign of letting up, with Air France pilots joining rail workers, rubbish collectors and oil refinery workers in industrial action.
The strike by a quarter of the company’s pilots will hit 20 percent of flights on Monday, Air France said, but disruption to Euro 2016 has been limited so far.
The strike is set to continue until Tuesday, when unions have organised nationwide rallies to protest government labour reforms.