Russia issued the announcement on Saturday as most of its diplomatic staff prepared to leave Georgia after Tbilisi accused four Russian army officers of spying and sent police to surround Russian army headquarters in the Georgian capital.
Under a bilateral agreement there was supposed to be a phased withdrawal of Russian forces from Georgia.
A spokesman for the defence ministry said the pull-out had been suspended because the security of Russian troops as they crossed Georgia could not be guaranteed.
The row erupted on Wednesday when the small, former Soviet state arrested four Russian army officers, accused them of spying and deployed police around the Russian army building in Tbilisi.
Russian officials said on Saturday that a withdrawal of diplomats and their families from the Russian embassy in Tbilisi was continuing, leaving just a skeleton staff.
Mikhail Svirin, the embassy spokesman, said: "Practically all of the embassy staff will be evacuated today and just a minimum number will remain."
Georgian sources say there are about 2,000 troops in the two remaining Russian army bases in Georgia.
Georgia's relations with its old Soviet, and Tsarist, master soured after Mikhail Saakashvili, the Georgian president, came to power in the so-called "Rose Revolution" in 2003, preaching closer ties with the US and EU and starting a drive to join the Nato military alliance.
There has been a regular war of words between the two sides, usually focusing on South Ossetia and Abkhazia, the two breakaway regions in Georgia, where separatist administrations say they want to secede to Russia.