Sergei Shamba said the denial was because residents of the former Georgian republic "apparently have to get visas in the German consulate in Tbilisi."
Speaking at a meeting with representatives of the UN human rights commissioner, Shamba also said that, "Such actions are out of line with universal humanitarian principles and are a direct violation of Abkhazian residents' rights."
The German embassy is yet to comment.
Russia recognized Abkhazia and South Ossetia after last August's five-day war with Georgia, which attacked South Ossetia in an attempt to bring it back under central control. Most residents of both Abkhazia and South Ossetia had held Russian citizenship for several years before the war.
Russia's decision to recognize the republics was condemned by the United States and the EU. Nicaragua has so far been the only other country to recognize South Ossetia and Abkhazia.
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The main event of the third day of the 11th meeting of the Valdai International Discussion Club in Sochi was the closing session with President Vladimir Putin. The atmosphere was calm and open, despite the current political tensions and the Russia-West confrontation. The Russian president said that it corresponded to the spirit of the Valdai Club.