French President Nicholas Sarkozy, who brokered the ceasefire in Georgia, has urged Moscow to remove its troops quickly from the west of the country.
Phoning his Russian counterpart Dmitry Medvedev, he hailed Friday's pull-back of troops but said they should also leave Georgia's Black Sea Poti port and Senaki in the west.
Russia's military said earlier they planned to keep Poti, an important port, under their control.
Russia's four-day war with Georgia erupted after Tbilisi tried to retake its province of South Ossetia - which broke away in 1992 and was supported by Moscow - in a surprise offensive on 7 August.
The conflict left hundreds of people dead and created tens of thousands of refugees.
The first US ship carrying aid is due to dock in Georgia shortly.