Russia recognized the breakaway Georgian regions as independent states last month after a brief armed conflict with Georgia, which attacked South Ossetia on August 8.
On Wednesday, Russia signed friendship and cooperation treaties with South Ossetia and Abkhazia, pledging economic and military aid to them.
"The issue of [Russian] troops' deployment will be decided bilaterally in compliance with international law," Vladimir Putin said after a meeting with his French counterpart Francois Fillon.
Russian Foreign Minister Sergei Lavrov earlier said a total of 7,600 troops would be deployed in Abkhazia and South Ossetia, more than twice the size of its peacekeeping contingents before the armed conflict with Georgia.
Fillon said his country would deploy 40 monitors in Georgia's "buffer zone" near South Ossetia and Abkhazia, as part of the EU mission of 200 observers.
"The European Union has decided to send up to 200 monitors," the premier said. "France will send about 40 people" into the region.
A European diplomatic source said on Tuesday that France would send 76 monitors to the mission, led by the EU's special representative for Georgia, Pierre Morel.
Once the EU mission has been deployed Russia will have 10 days to complete a full troop pullout from undisputed parts of Georgia.
