Hosts Russia knocked 2010 World Cup winners Spain out of the tournament to reach the quarter-finals for the first time since the break-up of the Soviet Union in 1991.

"Enthusiastic and epic assessments of yesterday's triumph are understandable from the emotional point of view. If you look at the streets of many Russian cities, including Moscow, in many respects it was comparable to footage from May 9, 1945, with the exception of the fireworks," Peskov told journalists.

He added that "sport unites, not separates" people.

"It was a fair game, and the one who is currently stronger wins in the fair game," Peskov said.

Russia will next face Croatia in the last eight match on 8 July (AEST).