Russia angrily dismisses a warning from Nato that normal relations are impossible while its troops remain inside Georgia.
US Secretary of State Condoleezza Rice on Nato's message to Russia
Foreign Minister Sergei Lavrov accuses Nato of bias and trying to save the "criminal regime" in Tbilisi. He insists Russia is not occupying Georgia and has no plans to annex South Ossetia.
President Dimitri Medvedev says that in the next few days, Russian troops will be pulled back to the positions agreed in the ceasefire plan.
He tells his French counterpart, Nicolas Sarkozy, that by Friday, part of the contingent will be pulled back to the security zone inside Georgian territory, along the South Ossetian frontier. The remainder will be withdrawn to South Ossetia and to Russia.
Earlier, Russian troops were seen leaving the Georgian town of Gori, but BBC correspondents on the ground say there are still several artillery positions and checkpoints in place.
In an apparent goodwill gesture, Russia exchanges 15 Georgian prisoners for five of its own troops at a Russian checkpoint near Tbilisi.
It is unclear whether Russia has begun to pull back troops from Georgia, despite pledges to do so, with the two sides issuing contradictory statements.
Russia says it will pull troops out of Gori and other Georgian towns
Georgian officials say there is no evidence that Russian troops are leaving their territory, but a spokesman for the Russian defence ministry says the redeployment has begun and will be completed within days.
However, Russian troops remain stationed near the Georgian capital, Tbilisi, with Moscow saying it has the right to keep some troops as peacekeepers in a buffer zone around South Ossetia.
Nato foreign ministers prepare to hold an emergency meeting on Tuesday to discuss the crisis, with the US backing efforts by both Georgia and Ukraine to join the alliance.
US Secretary of State Condoleezza Rice says the West must deprive Russia of any strategic victory from its assault on Georgia.
Russian President Dmitry Medvedev, in a phone call to French President Nicolas Sarkozy, says his forces will begin withdrawing from Georgia on Monday.
Russian troops are still stationed deep inside Georgia
However, Mr Medvedev indicates that additional troops sent to Georgia will withdraw to South Ossetia, rather than to their pre-conflict positions in Russia as agreed in a French-brokered ceasefire signed by both sides.
German Chancellor Angela Merkel goes to Tbilisi to show solidarity with Georgian President Mikhail Saakashvili.
After their talks, Ms Merkel says Georgia will become a Nato member, but stands by Germany's decision at the Nato summit in April to block a timetable for membership.
She calls on Russian troops to withdraw from Georgia, and says everyone accepts that the security zone set up by the Russians deep inside Georgian territory is temporary.
Georgia's President Mikhail Saakashvili signs an EU-brokered ceasefire with Russia after nearly five hours of talks with the US Secretary of State, Condoleezza Rice.
Russian forces have gathered around the Georgian port town of Poti
In angry comments, Mr Saakashvili says his country will never accept any loss of its territory, and he accuses the West - especially European countries - of inviting Moscow's military action by failing to offer his country Nato membership earlier this year.
At a joint news conference in Tbilisi, Ms Rice says Russia now has to withdraw from Georgia immediately.
The French mediators say Russian President Dmitry Medvedev has promised that Russia will sign the deal and respect its commitment to pull out its troops.
Earlier, in a hardening of rhetoric, President George W Bush accuses Russia of "bullying and intimidation" and warns that Moscow must honour its pledge to withdraw from Georgia.
German Chancellor Angela Merkel, meanwhile, meets Mr Medvedev in the Russian resort town of Sochi. She says some of Russia's actions have been "disproportionate" and that the presence of Russian troops in Georgia "is not sensible".
Mr Medvedev says he cannot see the people of South Ossetia and Abkhazia wanting to be a part of Georgia now.
Moscow is not against the idea of having international peacekeeping forces in the two regions, he says, but the people living there only trust Russian peacekeepers.
In Georgia, a BBC correspondent reports seeing Russian troops, armoured vehicles and helicopters at a naval dockyard in the port town of Poti, where the aim seems to be to destroy or remove Georgian military equipment. Russian forces are also reported elsewhere in Georgia, including around the towns of Gori and Senaki.
The first shipments of US humanitarian aid arrive in Georgia, with officials stressing Washington's commitment to its Georgian ally and promising continuing and regular shipments.
Russian troops took to the streets of Gori "to secure law and order"
On the ground, residents of Gori, the Georgian town at the centre of the crisis, report a quiet night and an increase in security with the town under the control of Russian paratroopers.
A Russian commander in the region confirms that his troops are beginning the process of handing back control of Gori, inviting Georgian police into the town to help restore law and order.
But a series of explosions around the town suggest the situation there remains volatile, and the Russians confirm they are not yet in a position to withdraw their troops.
In Moscow, Russia's president and foreign minister outline their visions for the resolution of the conflict with Georgia. President Dmitry Medvedev, meeting the South Ossetian and Abkhazian leaders, says Moscow will respect whatever course of action the two leaders, who head pro-Russian separatist movements, decide upon.
Russian Foreign Minister Sergei Lavrov is more blunt, telling reporters that any peace deal making reference to Georgian territorial sovereignty would be taken by the Abkhazians and South Ossetians as "a deep human insult".
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