France's interior minister called on tough sanctions against England and Russia after violent clashes in Marseille and urged hosting cities to consider a ban on alcohol around match days.
"It is absolutely necessary that the national federations whose supporters create incidents of this nature be punished for what happened inside the stadium, and also outside," Bernard Cazeneuve told a news briefing.
Cazeneuve said he asked police chiefs in nine hosting cities to take all measures to prevent the sale, consumption and transportation of alcohol on the day before a fixture and on the match day.
Anybody arrested for violent incidents could also be banned from all stadiums, fan zones and popular public areas in all host cities, he added.
Republic of Ireland boss Martin O'Neill described the ugly scenes as "shocking" and "tragic".
“The scenes down in Marseille are pretty tragic," he said. "They're something that we thought we might not see for quite some considerable time at any part of the tournament, but to start off on that note, it's unedifying, it's pretty shocking.
"To start off on that note, it's unedifying, it's pretty shocking." - Martin O'Neill
“UEFA have come out and condemned it in very strong language and I think everybody feels the same. It's a poor start to the competition, I hope it can be rectified and sorted out.
“People are talking about maybe segregation wasn't strong enough, but do you know what? If people are setting out for trouble, I think they'll cause it regardless and from the pictures that we saw, it was pretty disconcerting.
Robbie Keane echoed his managers sentiments, airing his disappointment at behaviour that coud see both countries removed from the tournament: “If it cost you your place at the tournament, it would obviously be disappointing because you work so hard to get here as a team, as a nation and then you see something like this. It's not great to see.
“They let everybody down. You have to say there's only a select few that always ruin it for everybody else, so it's very, very disappointing to see.”