TSKHINVALI, Georgia (Reuters) - Georgia offered Russia a ceasefire and peace talks on Sunday after pulling troops back from rebel South Ossetia’s capital, and mediators began a mission to end the internationally condemned fighting.

Some fighting still gripped parts of the Caucasus region, however, and Russia demanded an unconditional Georgian withdrawal.

French Foreign Minister Bernard Kouchner arrived in Tbilisi at the head of an international team of mediators, the first top level diplomatic mission to fly to the region in an attempt to stem the bloodshed. It was due to move on to Moscow on Monday.

After meeting Georgian President Mikheil Saakashvili, Kouchner said a “controlled withdrawal of the troops” was his main priority.

“Coming back to the table, negotiations, peace talks, a political solution. That’s it. Easy to say, very difficult to do,” Kouchner told journalists in Tbilisi.

The United States maintained its strong criticism of Russia, condemning its “disproportionate and dangerous” military action.

Russian troops and tanks took control of Tskhinvali, the region’s devastated capital, early on Sunday after a three-day battle. Moscow said 2,000 civilians were killed and thousands made homeless in a “humanitarian catastrophe”.

There has been no independent confirmation of the number of dead and wounded throughout the region.

The simmering conflict between Russia and its small, former Soviet neighbor Georgia erupted late on Thursday when Georgia sent forces into South Ossetia, a small pro-Russian province which threw off Georgian rule in the 1990s.

Russia, which had provided support to the separatists and had peacekeepers stationed in the province, responded by pouring troops and heavy amour south through the Caucasus mountains into South Ossetia to drive back the Georgians.

The conflict alarmed the West, which views Georgia as a valuable, if volatile, ally because of its strategic location on an energy transit route carrying oil from the Caspian to Europe.

Saakashvili appeared smiling but disheveled to meet Kouchner, before showing him the night-time view of Tbilisi from a hillside.

“It is the most surreal world crisis I could ever imagine,” the Georgian leader told reporters.

FRENCH PRESIDENT TO VISIT MOSCOW

The office of French President Nicolas Sarkozy, current holder of the European Union’s rotating presidency, said he would also visit Moscow in the next few days.

The French leader has produced a peace plan focusing on both sides pulling back to areas they held before the hostilities.

At the U.N., Moscow and Washington traded barbs in the Security Council.

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U.S. ambassador Zalmay Khalilzad suggested Russia was seeking “regime change” by saying Saakashvili should leave office while Russian envoy Vitaly Churkin obliquely suggested some leaders became “obstacles” to their people.

The United States said any further Russian escalation of the conflict could have a “significant, long-term impact” on relations and called on Russia and Georgia to cease hostilities and return to their pre-conflict positions.

President Dmitry Medvedev said Georgia must withdraw from South Ossetia and formally pledge not to attack the region.

Meanwhile, fighting continued. A Reuters reporter in the town of Gori, just south of South Ossetia, reported heavy bombardment of areas around Tskhinvali on Sunday evening, although it was not clear who was firing.

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Russian planes again bombed the Tbilisi military airport and a nearby aviation plant. One bomb exploded near the runway of the civilian international airport, although Moscow denied targeting that facility.

A Reuters photographer entering Tskhinvali with Russian troops on Sunday saw dead Georgian soldiers lying in the streets and the ruins of buildings devastated in the fighting.

Georgia and Russia have accused each other of causing widespread civilian casualties since the fighting began.

State-controlled Russian television repeatedly spoke of a “humanitarian catastrophe” in South Ossetia after the Georgian attack, with more than 2,000 dead and thousands homeless.

A Georgian government source said on Sunday 130 Georgian civilians and military personnel had been killed and 1,165 wounded, many because of Russian bombing inside Georgia. Russia denied hitting civilian targets.

DEVASTATION

Russian television showed what it said were pictures from Tskhinvali of burnt-out buildings, wounded civilians receiving medical treatment in dilapidated basements and weeping mothers complaining of a lack of food and water.

“It started with severe bombing with artillery and planes and helicopters. Our boys, with their guns, could do nothing,” resident Alla Dzhiloyeva told RTR state television by phone.

“They bombed us so may times all the houses are destroyed... On one street there is only one wall left.”

Pictures on NTV television showed Tskhinvali’s main hospital in ruins and most of its 200 patients crammed into the basement. Patients, many wincing, underwent treatment on tabletops in what looked like unsanitary conditions.

Russian Prime Minister Vladimir Putin cut short his visit to the Olympics on Saturday and flew to a field hospital in North Ossetia, visiting wounded troops and evacuees, and denouncing what he termed Georgia’s “crimes against its own people”.

Putin later briefed a Moscow-bound Medvedev on his trip, in a televised exchange which underlined Putin’s continued dominance of Russian politics and government.

Potentially widening the conflict, Sergei Bagapsh, the leader of Abkhazia, another separatist region on Georgia’s Black Sea coast, said he had ordered 1,000 troops to push Georgian forces out of the Kodori Gorge, a strategic pocket of territory. He called up reservists.