Far-right nationalism has been an ongoing concern in Russia for decades, but has been on the upswing in recent years, gaining membership at a rate that has shocked many Russians.
They've held rallies in the capital, bearing swastikas and chanting "Russia is for Russians".
"All Nazis, independent of where they come from... they simply undermine the cultural foundations of our state," said the Russian President.
In December of 2010 Moscow authorities were overwhelmed by 7,000 right-wing nationalists who gathered outside the Kremlin and began beating people of non-Slavic appearance.
Russian Prime Minister Vladimir Putin joined Medvedev in denouncing the racism calling it "xenophobia", which is unacceptable in the modern inter-connected world.
Russia is due to host the 2018 soccer World Cup and the latest incidents have raised concerns about the safety and security of non-white visitors to the country.
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