The Prime Minister said he was "appalled" by the racist scenes at the end of the England Under-21 2013 European football match against Serbia last night, according to Downing Street.
David Cameron's official spokesman said the government was giving its full backing to a Football Association complaint over alleged racist comments by Serbian players.
Sport minister Hugh Robertson has written to UEFA president Michel Platini urging an investigation.
Britain expects "tough sanctions" if racism is proved, said the spokesman.
– David Cameron's official spokesman
"He was appalled by the scenes that we have seen in Serbia. We are determined to stamp out racism internationally and at home and we are giving our full backing to the FA's complaint on this issue.
"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.
"It is not good enough to say that people should shake hands and forget about it."