Güncelleme Tarihi:
Russia, which has more than 9,000 paratroopers and 350 pieces of armor in the rebel region, said the ultimatum expired at 0600 GMT, Interfax news agency reported.
The West, already alarmed by the speed at which the conflict between Russia and Georgia over South Ossetia has escalated, is worried fighting could spread to Georgia's other breakaway region Abkhazia.
The news agency quoted the head of the Russian peacekeeping force in Abkhazia, Sergei Chaban, as saying Russian forces were nearly ready for an operation to disarm Georgian troops in the area.
"If the ultimatum is rejected all necessary enforcement measures will be used," Chaban said.
A Georgian Interior Ministry spokesman replied: "We are not going to surrender any arms to the Russians."
Russian forces are now in control of South Ossetia's regional capital, Tskhinvali, after driving out Georgian forces.