The two leaders agreed in September that Russia's full withdrawal from Georgia would come not more than 10 days after the European Union deploys at least 200 observers in the "buffer zone" near South Ossetia and Abkhazia, which occurred Wednesday.
"Russia will fulfill all we outlined... We will do everything on schedule," the Russian leader told journalists after talks with Spanish premier Jose Luis Rodriguez Zapatero, which touched upon joint work to implement agreements reached between Moscow and Paris.
Russia launched a five-day military operation to "force Georgia to accept peace" after Georgian troops attacked breakaway South Ossetia on August 8, killing a number of Russian peacekeepers and hundreds of civilians.
Russia's response to the Georgian attack was labeled "disproportionate" by a number of Western powers. On August 26, Russia recognized South Ossetia and Abkhazia, another breakaway Georgian republic, as independent states.
Abkhazia and South Ossetia broke away from Georgia following the collapse of the Soviet Union in the early 1990s amid armed conflicts that claimed thousands of lives.
Despite a deterioration of relations between Russia and the United States after the recent conflict with Georgia, Medvedev said the two countries had no ideological differences that could lead to "a Cold War or some other kind of war."