Georgia's Deputy Foreign Minister Grigol Vashadze dismissed the treaties as legally void.
"Abkhazia and the Tskhinvali region are inseparable parts of Georgia," Vashadze told reporters in the Georgian capital. "The treaties signed in Moscow carry no legal force and contradict international law."
Eduard Kokoity, the South Ossetian leader, and Sergei Bagapsh, the leader of Abkhazia, signed the treaties with Medvedev.
Russia has said it will permanently deploy nearly 8,000 troops in the regions on a long-term basis.
Russia has pledged to withdraw all other forces now on Georgian territory outside South Ossetia and Abkhazia within 10 days of the deployment of EU monitors who are supposed to be in place by Oct. 1. But it is pushing to keep Western observers away from South Ossetia and Abkhazia.
Vashadze said that Georgia will demand a full Russian withdrawal from its territory, including both breakaway provinces, at an international conference set to open in Geneva in mid- October.
Last month's war and Moscow's recognition of the two regions have pushed Russia-West relations to the lowest point since the Cold War.
Nicaragua is the only other country that has recognized the independence of Abkhazia and South Ossetia.
Also yesterday, Russia issued an unusually harsh condemnation of the NATO chief's visit to Georgia, saying it showed a Cold War mentality and would further destabilize the region.
NATO's support for Georgia after last month's war with Russia last month can only be seen as "encouraging Tbilisi to engage in new reckless ventures," Russia's Foreign Ministry said.
NATO Secretary-General Jaap de Hoop Scheffer and envoys from all 26 member countries were in Georgia this week. The former Soviet republic is eager to join the Western military alliance, a step Russia strongly opposes.
In a message of support for Georgia, de Hoop Scheffer said Tuesday that its "road to NATO is still wide open."
"No other country will have a veto over that process, nor will we allow our strong ties to Georgia to be broken by outside military intervention and pressure," he said.