Russian sports minister Vitaly Mutko downplayed the clash between their fans and England supporters at the end of the 1-1 draw on Saturday.
Shortly after the final whistle, Russian fans broke past stewards to invade the England stands and throw objects at the Stade Velodrome in Marseille.
"Weak" security was to blame for the incident, according to Mutko, who is also the head of the Russian Football Union and has a senior role with FIFA.
"There was no clash... That's being exaggerated, in fact everything is fine here," Mutko told R-Sport. "When the match ended, there was no barrier between the fans. The British were upset, of course, but it all quickly dissolved.
"Such matches should be organised properly. It is necessary to separate the fans [at the stadium].
Mutko did vow to identity and punish fans who acted inappropriately, and criticised the prohibited launch of flares from the Russia fans' section.
"The bad thing is that there were firecrackers and flares," he said. "There were no nets. One must understand these things."
Aleksandr Shprigin, head of the Russia football fans' union, also denied the scenes were as bad as they appeared, telling the Russian government's RT television station "there was no clash."
"The entire English sector just got up and ran away. There were no scuffles, police were standing there," he said. "Everything is OK. The police are working well."
The Guardian reported that Russian state news service Vesti said the Russian fans were the ones under attack.
"Two hundred and fifty Russian fans repulsed an attack by several thousand English and forced them to flee," Vesti was quoted as reporting. "English fans started the fight by attacking our fans, but 250 Russians from different corners of our country did not flinch and repulsed the attack of the heavily drunken islanders."
Governing body UEFA will open disciplinary proceedings over the violence at the stadium, with Russia facing stronger sanctions than England.
England's Football Association called on fans "to act in a respectful manner and support England the right way."
FA spokesman Mark Whittle said, "The FA is very disappointed by the terrible scenes that we saw there and of course condemns such behaviour.''
He called on French authorities "to identify those involved in the troubles and deal with them appropriately and quickly."