Both sets of fans have been involved in clashes since the beginning of the tournament
Russian Foreign Minister Sergei Lavrov has attacked what he described as the "provocative actions" of England fans following clashes between the rival fans at the Euro 2016 championships in France.
The senior diplomat conceded it was "unacceptable to behave like some of our citizens", but said the "insults" directed at Russia could not be ignored.
"We cannot turn a blind eye to the fact that (the French) are trying to ignore the absolutely provocative actions of fans from other countries," the RIA agency quoted Mr Lavrov as saying in parliament on Wednesday, apparently referring to England fans.
"You probably saw the outrageous scenes on television of them trampling on the Russian flag and screaming insults directed at the Russian leadership and leading Russian athletes," he said.
Mr Lavrov also complained about the "absolutely unacceptable" detention on Tuesday of 43 Russian fans suspected of being involved in the violent clashes at the weekend. Fans were arrested after being told to get off a bus for document and ID checks.
He said French authorities had failed to inform Russian diplomats about the incident despite having an obligation to do so under international law. The French ambassador has been summoned to explain why.
Russia, whose fans fought with England supporters in Marseille at the weekend, earlier played against Slovakia in Lille - where English and Welsh fans have gathered ahead of their group game on Thursday.
Security in the city has been beefed up, with a senior police officer warning fans looking to start any trouble that "we are ready to fight against this violence".
More than 2,500 police, security guards and soldiers will be on duty over the next couple of days.
Russia has been handed a suspended disqualification from the tournament over crowd disturbances at Saturday's game against England.
UEFA has also fined the Russian football federation €150,000 (£119,000) and warned the team will be kicked out of the championships if there is any repeat of the violence which saw Russian fans charge at England supporters inside the Stade Velodrome.
Home Secretary Theresa May condemned the disorder in the House of Commons and echoed calls from Roy Hodgson and Wayne Rooney for England fans to behave.
Six England fans have been jailed in France, while another supporter was arrested on his return to the UK and has beenbanned from watching football for five years.
A small number of extra British police are being sent to France, while officers are working to identify 48 supporters involved in clashes.