Uefa has charged the Serbian and English football associations following the fracas at the end of the Under-21 football match between the two nations.
European football's governing body said it was instigating proceedings against the Serbian FA over the conduct of its players and supporters.
And proceedings are also being instigated against the English FA for the "improper conduct" of its players.
Earlier, Prime Minister David Cameron said he was "appalled" by the fracas.
He called on Uefa to impose "tough sanctions" if racism is proved. Its Control and Disciplinary Body will discuss the cases on 22 November.
England Under-21 defender Danny Rose, 22, has called for Serbia to be banned after claiming he was racially abused by fans in Krusevac on Tuesday.
He said he was subjected to monkey chants from the crowd throughout the game, starting in the warm-up, and then was confronted by Serbian players after England scored in the 90th minute.
Some fans ran on to the pitch and scuffles broke out as England celebrated a 1-0 win and Euro 2013 qualification.
But the Serbian FA has denied any forms of racism towards the England team.
It also said Rose behaved in an "inappropriate, unsportsmanlike and vulgar manner" towards their fans.
FA general secretary Alex Horne had earlier called on Uefa to "take the strongest possible action" against anyone guilty of violence and racist abuse at the end of the match.
"It is also clear that we must defend Danny Rose, who was sent off due to the frustration of being a target of racial abuse.
"No football team should be asked to play in any environment where racial abuse, violence and threatening behaviour is prevalent. We must question the validity of sending a team to Serbia in the future."
The government is giving its full backing to a Football Association complaint over alleged racist taunts, a spokesman for Number 10 said, adding that Mr Cameron "was appalled by the scenes that we have seen in Serbia".
"Clearly it is for Uefa to investigate this issue but we would expect tough sanctions. If we are going to stamp out racism from football, then it is no good giving derisory fines, as have been handed out in the past.
Sports minister Hugh Robertson has also written to the president of Uefa, Michel Platini, urging him to investigate the incident.
"The really important thing is that this is the time to have no more derisory fines, no more punishments that send out the wrong message," he said.
The chairman of the Professional Footballers' Association, Clarke Carlisle, said Serbia should serve a ban from European football.
"Serbia should be banned because it's a repeat offence," he told BBC Radio 5 live.
"Banning them for a start, from any tournament, would be progress but I think if it's significant - if it's a couple of tournaments - then that would cause that nation to address the issue that has deprived them of international competition."
Former England footballer Luther Blissett has also called for Serbia to be banned from football tournaments by Uefa.
"They should get a three, four-year ban and that's talking about at club level and international level in my opinion because that it the only way these countries will really start to look at it and say 'we have to do something about it'.
"Because they obviously don't see that they're doing anything wrong by abusing people the way they do."
England defender Nedum Onuoha was racially abused during the 2007 Under-21 European Championship game against Serbia in the Netherlands, for which Serbia were fined £16,000 by Uefa.