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During his telephone conversation with British Prime Minister Gordon Brown, Medvedev said "Russia fully abides by the Medvedev-Sarkozy principles and noted that they remain fully valid," the Kremlin said.
Russia called for "more OSCE (the Organization for Security and Cooperation in Europe) observers to be deployed in the buffer zone," as well as an impartial international monitoring of the current Georgian leadership, Medvedev said.
Moscow hoped to maintain constructive dialogue with the European Union (EU) and other international organizations, he added.
The Russian president also "explained to Brown why Russia has decided to recognize the independence of South Ossetia and Abkhazia," said the Kremlin.
Some member states of the EU prompted to impose sanctions on Russia at an emergency EU summit, which is scheduled for Monday in Brussels to discuss the Georgia crisis.
On Tuesday, Medvedev signed decrees recognizing the independence of South Ossetia and Abkhazia, which broke from central Georgian rule during wars in the early 1990s.
Georgia, a former Soviet republic and a staunch U.S. ally, has long been at odds with Russia over the two breakaway regions and its own bids to join NATO and the European Union.
Earlier this month, Georgia sent in troops to reclaim South Ossetia, triggering a military counter-offensive from Russia. The conflict ended with a ceasefire agreement between Tbilisi and Moscow brokered by France.