Russian Defense Ministry officials said Saturday the decision was made because the troops' safety could not be guaranteed as they crossed Georgian territory.
Russia has agreed to withdraw its troops from the two military bases by 2008.
The crisis began Wednesday when Georgia arrested five Russian army officers for allegedly spying. One was released, but four are still in custody and facing trial. Georgia said Friday it has not ruled out deporting the servicemen.
Russia denies the officers are spies, and has demanded their release. Moscow recalled its ambassador to Georgia in protest, and is continuing the evacuation of most of its embassy personnel today.
At the United Nations, Russian officials Friday rejected proposed U.S. changes to a draft Security Council statement expressing concern over Georgia's actions. Discussions could continue today.
At a meeting with NATO in Slovenia Friday, Russia's defense minister accused NATO members from Eastern Europe of illegally supplying Soviet-made arms to Georgia.
Georgia has long accused Russia of backing separatists in two pro-Russia breakaway areas of the country, Abkhazia and South Ossetia. Russia deployed peacekeepers in the regions after they declared independence from Tbilisi in the early 1990s.
Relations between Russia and Georgia have become increasingly strained since the 2003 election of Georgian President Mikhail Saakashvili, who is steering the former Soviet republic toward NATO and European Union membership.
Some information for this report was provided by AFP, AP and Reuters.