Grushko met with Miroslav Kostelka, the ambassador for the Czech Republic, which holds the rotating EU presidency, as well as with Sweden's ambassador to Russia, Tomas Bertelman, and European Commission Moscow office chief Marc Franco.
"Grushko expressed concern in connection with the build-up of a Georgian military presence on South Ossetia's borders," the Foreign Ministry said in a statement.
"The increased activity of their [Georgian] special units has been reported on the eastern part of the South Ossetian border," the statement said.
South Ossetia and Abkhazia, another breakaway republic, were recognized as independent states by Russia last August. The move came shortly after a Georgian assault on South Ossetia to regain control of the province and a subsequent five-day Russian military operation to "force Georgia to peace."
Abkhazia and South Ossetia split from Georgia in the early 1990s, and most residents of both republics have had Russian citizenship for a number of years.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.