Combat troops are set to withdraw but peacekeepers will remain
The UN Security Council is deadlocked over the situation in Georgia with the US and Russia rejecting rival resolutions on the crisis.
Washington says it is prepared to veto a Russian resolution seeking to implement a six-point ceasefire plan.
Russia has reiterated its opposition to a rival French text reaffirming Georgia's territorial integrity.
Russian says its troops will leave Georgia on Friday but 500 will stay in a "buffer zone" around South Ossetia.
Local reports suggest Russian troops are still dug in at positions inside Georgia, but there has been some movement around the town of Gori, which Russia has promised to leave by 1600 GMT.
"They are going, but extremely slowly," Vova Djugali, police chief at the nearby village of Igoeti, told AFP news agency.
Meanwhile, a Nato spokeswoman says Russia's defence ministry has decided to halt all military co-operation with the bloc to protest at what Moscow calls the alliance's biased, pro-Georgian view of the conflict.
The move by Moscow followed a Nato statement that there would be no "business as usual" with Moscow unless its troops pulled out of Georgia.
A White House spokesman said President George W Bush expected Russia "to abide by its agreement to withdraw forces".
Georgian President Mikhail Saakashvili has told the BBC the Russians are still consolidating their hold on parts of his country, and he again accused them of trying to paralyse the Georgian economy.
Russia fought a four-day war with Georgia after it tried to retake the Moscow-backed breakaway province of South Ossetia on 7 August, following days of clashes with separatists.
The counter-offensive by Russia, which has had peacekeeping troops in South Ossetia since the early 1990s, took its troops beyond the province into Georgia's heartland.
President Saakashvili told the BBC's Today programme Georgia would never accept what he called Russia's "annexation of its territory".
He renewed claims that Russia had been planning to invade Georgia long before Tbilisi's own assault on South Ossetia.
He also warned that Russia's involvement in South Ossetia, Abkhazia and Georgia were intended to send a strong message to the West.
"If Nato fails now to come up with a united response, nobody's safe, even if they are in Nato already," he said.
"It's all about reconsidering the role of Nato, the role of international law and borders in this part of the world. This is no longer about Georgia anymore.
"Russia decided to win war with Nato without firing a single shot at it."
There is no sign of agreement over the rival resolutions, one backed by Russia and the other by Western European countries and the US, the BBC's Laura Trevelyan reports from New York.
A top US general is in Tbilisi to inspect the damage to Georgia's army
France circulated a draft resolution on Tuesday, calling for an immediate Russian withdrawal from Georgia and reaffirming Georgia's territorial integrity.
Russia rejected this because it said Georgia's breakaway regions of South Ossetia and Abkhazia wanted independence.
Moscow circulated its own draft calling on the Security Council to endorse the six-point peace plan brokered by France and agreed by Moscow and Tbilisi.
"Our draft resolution is a reconfirmation of the six-point agreement, and there's no territorial integrity in the six principles," said Russia's UN Ambassador, Vitaly Churkin.
Now Russia's ambassador says his resolution is going into its final form, so it can be voted on.
Some elderly Georgians were evacuated from S Ossetia on Thursday
But the US and its allies insist Russia is not respecting the ceasefire plan because it is not withdrawing from Georgia quickly enough.
The US Deputy Ambassador to the UN, Alejandro Wolff, said under the circumstances he thought America would be prepared to oppose Russia's resolution.
Russia's land forces commander, Gen Vladimir Boldyrev, has said all Russian combat troops will move back from Georgia proper to South Ossetia by the weekend.
Most of the soldiers sent to the region as reinforcements will return from South Ossetia to Russia within 10 days, he added.
However, Moscow will retain 500 peacekeepers in a security zone stretching 7km (four miles) beyond the border of South Ossetia into Georgia proper - a move Tbilisi says is unacceptable.