Russian President Vladimir Putin says that hosting of the World Cup has helped debunk stereotypes about the country.
After safety concerns and fears of discrimination, there have so far been no major non-footballing incidents at the tournament.
At a meeting with FIFA president Gianni Infantino and former footballers at the Kremlin, Putin said the tournament and its coverage on social media had "helped break many stereotypes about Russia."
"People have seen that Russia is a hospitable country, a friendly one for those who come here," he said. "I'm sure that an overwhelming majority of people who came will leave with the best feelings and memories of our country and will come again many times."
Moscow's streets have been flooded with fans and locals, not least due to Russia's own progression at the tournament.
"I was told people, police in the Red Square are smiling," Infantino said. "When they are asked for some information, they are very friendly. This is great. This is exactly what Russia is. This is the new image that we have about Russia."
Russia coach Stanislav Cherchesov has said Putin has been in touch to support the home players.
"He has been calling me, he called me before and after the game with Spain," Cherchesov said. "When the president supports you that makes us comfortable and this is an extra boost for us in terms of motivation."
After entering the tournament as the lowest-ranked side, Russia made it through to the knockout stage for the first time in post-Soviet history, upsetting Spain in the round-of-16.
Russia will face Croatia in the quarterfinals in Sochi on Saturday.