Fifteen Georgian soldiers were exchanged for five Russian soldiers
Nato foreign ministers are meeting in Brussels for emergency talks to discuss how the alliance should respond to Russia's military action in Georgia.
UK Foreign Secretary David Miliband has said Nato ministers agreed Russia had broken international law in its conflict with Georgia.
The OSCE says both Russia and Georgia have now agreed to let 20 military observers in Georgia.
A column of Russian tanks has been seen pulling out of the town of Gori.
Mr Miliband, who left the Nato meeting early to fly to Tbilisi, said the outcome showed real Nato unity: "The Nato membership was clear that Russia had violated international laws as well as the rules of the international game."
Russia had to abide by the ceasefire agreement and withdraw its troops from Georgian soil, he said. The alliance was set to offer new practical and political support for the government in Tbilisi, and Georgia would be given a clear route map to Nato membership, he said.
Russia's refusal to withdraw its forces ahead of this meeting had been a big unifying force within the alliance, he added.
Earlier, officials in Tbilisi said there was no evidence that Russian troops were leaving Georgian territory. But Moscow has said that while it has started to pull back its troops in line with the ceasefire deal, Georgia has not.
A Russian military spokesman did not confirm that Russian forces had taken control of the commercial port at Poti on Georgia's Black Sea coast - as alleged by Georgian authorities earlier on Tuesday - but said that at least 20 armed men in Georgian uniforms had been detained there.
In Brussels, the Organization for Security and Co-operation in Europe said 20 observers would supplement the current nine observers already based in South Ossetia, according to the organisation's chairman, Finnish Foreign Minister Alexander Stubb, who was speaking on the sidelines of the Nato talks.
Earlier in an apparent gesture of goodwill, Russian and Georgian troops exchanged prisoners at a checkpoint near the Georgian capital, Tbilisi.
Fifteen Georgian soldiers for five Russian soldiers took place at a Russian checkpoint in Igoeti, about 30km (18 miles) away from Tbilisi, the Georgian capital.
The BBC's Helen Fawkes, at the scene, saw two injured Russians, brought to the checkpoint by ambulance, carried on stretchers by Russian soldiers before being put onto waiting helicopters and taken away.
Two of the Russians were pilots who had been shot down, Georgian officials told the BBC.
A few minutes' walk from the site of the exchange, a noisy protest was held by several hundred Georgians demanding that Russia withdraw its forces, our correspondent adds.
The conflict broke out on 7 August when Georgia launched an assault to wrest back control of the Moscow-backed breakaway region of South Ossetia, triggering a counter-offensive by Russian troops who advanced beyond South Ossetia into Georgia's heartland.
A ceasefire was signed at the weekend, with Moscow pledging to begin pulling back its troops on Monday, but correspondents say there has so far been little sign of any large-scale force withdrawal.
As Nato's 26 foreign ministers meet in Brussels, the BBC's Jonathan Marcus says there is disagreement among the alliance as to how to respond, so the focus will be on where members can agree.
HAVE YOUR SAY
The sight of GWB [US President George Bush] complaining about Russia's "disproportionate use of force" is hilarious
It is thought that in one camp, the UK, Canada, the US and most Eastern European member states will seek a tough stance on Russia, but most of Western Europe, led by France and Germany, is expected to be more cautious of harming ties with Moscow.
Flying to the Nato meeting, Ms Rice told reporters on Monday: "We have to deny Russian strategic objectives, which are clearly to undermine Georgia's democracy, to use its military capability to damage and in some cases destroy Georgian infrastructure and to try and weaken the Georgian state."
Nato is also expected to offer more humanitarian aid and proposals on how to rebuild Georgian infrastructure damaged in the conflict.
Washington has denied claims from Moscow that it is out to wreck the Nato-Russia Council - a consultative panel set up in 2002 to improve ties between the former Cold War enemies.