Shota Utiashvili, Georgia's interior ministry spokesman, said: "I can confirm that the five Russian checkpoints on the Poti-Senaki axis have been removed. The Russian troops are heading towards Abkhazia."
Alexander Lomaia, the chief of Georgia's security council, said that about 250 soldiers and more than 20 armoured vehicles had withdrawn.
On Monday, Moscow agreed to withdraw its troops from positions in areas of Georgia outside the separatist regions of South Ossetia and Abkhazia within a month.
Hundreds of soldiers have been manning checkpoints and carrying out patrols in strategically important areas of the country since Russian forces moved in to support the South Ossetian separatists.
Matthew Collin, a journalist in the Georgian capital, Tbilisi, told Al Jazeera that interior ministry officials were saying that more than 20 Russian checkpoints remained despite Saturday's movements.
Russia has also said it will keep about 7,600 troops in South Ossetia and Abkhazia, which the Kremlin last month recognised as independent states.
|Russian troops move out near Zugdidi [Reuters]
Dimtry Medvedev, the Russian president, said the withdrawal agreement was made possible after the EU offered guarantees that Georgia would refrain from any use of force against the regions.
The accord depends on the deployment of an international monitoring force, including 200 members from the European Union
Meanwhile, Georgia's president has come under fire from a former political ally for his handling of events in the run-up to the conflict.
Nino Burjanadze, a former speaker of parliament, said on Friday: "There is a time for tough questions. Of course, what happened was a Russian provocation, but we need to know whether it was possible to not yield to this provocation."
She also called for an independent investigation to ask "tough questions" about Mikheil Saakashvili's leadership.
Russian forces moved in after Georgian troops began a heavy bombardment of Tskhinvali, the capial of South Ossetia, on August 8.