Led by Dutch trainer Guus Hiddink, the young Russia squad surprised many fans by reaching the semifinals, where they lost to an experienced Spanish side 3-0.
"You have accomplished a sporting feat and no matter how pompous it may sound it is really so," the president said.
Russia were outclassed by Spain in their opening game at the tournament on June 12, losing 4-1, but won their next three matches to reach the last four. Those victories, against Greece, Sweden and, most notably, the Netherlands, had the soccer world hailing such previously "unknown" names as Andrei Arshavin, Yury Zhirkov and Roman Pavlyuchenko.
The president said he was pleased and honored to meet with the Euro-2008 semifinalists and bronze medal winners as he had closely watched all the games just like the whole of Russia.
"Just like the rest of our people I attentively followed all developments and rejoiced in all your successes. Improving from game to game, you demonstrated outstanding physical fitness and team spirit," Medvedev said.
"The country was not disappointed that you did not take first place and won the bronze. It was a colossal effort and only you know how tough it was," he added.
The Russian players thanked the president for his kind words and Sergei Semak, the captain, gave him a football and a team jersey with the president's name.
Hiddink, who also attended the reception, said he was honored to be invited by the Russian president and glad and proud that he had been part of changing the attitudes of Russian soccer fans, who again believe in their national team.
Last week on arrival in Moscow after the championship, Hiddink said that Russia should be proud of its players, because he had set them the task of qualifying from the group stage and they had gone one better by reaching the semifinals.
Indeed, Hiddink has transformed the Russian side, rendering it virtually unrecognizable from earlier, ultra-cautious incarnations. The attacking, open soccer demonstrated by Andrei Arshavin and co against Sweden and the Netherlands has done much for the image of the national team, and even stirred global interest in the country's Premier League.
The semifinal defeat was Hiddink's third at a major tournament, his Dutch team losing to Brazil on penalties in 1998, and his South Korean side going out to Germany in 2002.
Russia's soccer chief, Vitaly Mutko, told Medvedev that the Russian team will now focus on qualifying for the 2010 World Cup in South Africa.
Russian failed to qualify in 2006 for the World Cup in Germany. And in 2002 the team did not make it out of the group stage in Japan and South Korea.
Finland, Wales, Azerbaijan, Lichtenstein and Germany, which lost to current European Champions, Spain, in the Euro-2008 final, are the other teams in Russia's World Cup qualifying group.
