The statement came after Russia withdrew its troops from observation posts between Senaki and Poti on Saturday, which is two days ahead of the deadline set by Dmitry Medvedev and Nicolas Sarkozy.
"The Russian party expects the same strict and conscientious approach of all parties concerned, first and foremost of the Georgian leadership, as well as of the EU," the statement said.
Medvedev and Sarkozy also agreed on September 8 that Russia's full withdrawal from Georgia will 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 under the new agreement is set to happen by October 1.
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.