A ceasefire appears to have been agreed to by both Russia and Georgia.
Georgian President Mikheil Saakashvili says he has signed a ceasefire with Russia although he's stressed it is not a permanent solution.
And United States officials say the Russian Foreign Minister Sergei Lavrov has pledged that Moscow will implement the ceasefire agreement.
He gave the assurance after the US Secretary of State Condoleezza Rice phoned him following a visit to Georgia.
Dr Rice demanded Russia withdraw at once but the Russian military is still reported to be operating deep in Georgia.
The agreement was brokered by France.
Mr Saakashvili stressed that the ceasefire was not a permanent solution and said his country would never accept any loss of its territory.
Russian President Dmitri Medvedev says only Russia can guarantee peace in the region.
The crisis began when Georgia attacked South Ossetia on 7 August, sparking Russian retaliation. The separatist region is backed by Moscow.
Russian forces have routed Georgian troops in a six-day war and continued into Georgia.
A military convoy reportedly advanced to a village 45km from the capital, Tbilisi, on Friday.
Top US officials have invoked memories of the Soviet Union's occupation of Eastern Europe during the Cold War.
Georgia is an ally of the United States and aspires to join NATO.