"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 [when Russia celebrated the World War II victory], with the exception of the fireworks," Peskov told journalists.
The comment referred to the Sunday's round 16 match, during which hosts Russia knocked 2010 World Cup winners Spain out of this summer's tournament to reach the quarter-finals for the first time since the break-up of the Soviet Union in 1991.
"It was a fair game, and the one who is currently stronger wins in the fair game," Peskov said, adding that "sport unites, not separates" people.
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Speaking about the president's reaction to the game, the spokesman noted that Vladimir Putin supported the Russian national football team "with all his heart".
"He [Putin] supported the team just like all the Russians — with all his heart," Peskov told journalists.
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Russia will next face Croatia in the last eight match, which will be played in the Black Sea resort of Sochi on Saturday. When asked if the Russian president will attend the upcoming game, the spokesman replied that Kremlin was still unaware about the issue.
"I don't know. Initially, the president's schedule… allowed for the president's attendance of the opening match and the closing match of the tournament. You know that the head of state surely has many responsibilities, which often keep him from attending certain events, but I can't give a precise answer to this question yet," Peskov told journalists when asked if Putin plans to attend the Russia-Croatia match.
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As head of Moscow's Security and Anti-Corruption Department Vladimir Chernikov told Sputnik on Monday, more than 100,000 Russians and foreign tourists celebrated Russia's victory.
"The total number of those who partied in the center of Moscow is more than 100,000 people… People went to the city center, and the joy was universal. It is understandable, such things do not happen often," Chernikov said.
Moscow Mayor Calls Luzhniki 'Lucky Arena' for Russia
Meanwhile, Moscow Mayor Sergey Sobyanin called the city's Luzhniki Stadium a "lucky arena" for the Russian national football team.
"I should say that the Luzhniki Stadium is a very lucky arena — two games and two good, beautiful victories [for Russia]," Sobyanin said, adding that the team "have done the impossible" and urged everyone to continue rooting for them.
Russia also thrashed Saudi Arabia 5-0 at the Luzhniki Stadium in the opening match of the World Cup on June 14.
The 2018 FIFA World Cup kicked off on June 14 and will continue until July 15, with the matches being played in 11 cities across Russia.