FIFA charged World Cup host Russia with fan racism Tuesday, less than two months before the tournament begins.
Monkey chants were aimed at black French players, including Paul Pogba, during France's 3-1 friendly win over Russia in St. Petersburg last month.
"Disciplinary proceedings have been opened against the Russian Football Union for this incident," FIFA said.
Russian Deputy Prime Minister Arkady Dvorkovich, who is overseeing World Cup preparations, told state news agencies Tuesday that Russia was cracking down on racist fans.
"We'll do anything so there are no discrimination cases," he said. "But if that happens ... there should be zero tolerance for these people."
The RFU said it is cooperating with the FIFA investigation.
"A request has been made to the Interior Ministry to identify several persons who were involved in these incidents," RFU anti-discrimination officer Alexei Smertin was quoted as saying Monday by the Tass news agency. "If these people's guilt is proven, then there's a high likelihood they won't be allowed to attend World Cup and Russian league games."
Russia was previously charged with racist behavior by its fans at the last two European Championships. On both occasions, the RFU paid a fine.
It's the third racism case this season at St. Petersburg Stadium, which will host a World Cup semifinal match. Zenit St. Petersburg has twice faced UEFA charges for racism by its fans in Europa League games.
Zenit fans flew a banner praising convicted war criminal Ratko Mladic when playing a Macedonian club in November and are accused of using a racially charged term to mock an injured black player in a game against Leipzig. The second case is due to be heard by UEFA on May 31, two weeks before the World Cup begins.