United States Vice-President Dick Cheney has called Georgian President Mikheil Saakashvili to say "Russian aggression must not go unanswered," the vice-president's office said.
The United States has accused Russia of seeking regime change in Georgia as the US pushes the UN Security Council to call for a ceasefire in the widening, bloody Caucasus conflict.
The simmering conflict between Russia and its small, former Soviet neighbour 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.
Moscow said 2,000 civilians were killed and thousands made homeless in a "humanitarian catastrophe" but there has been no independent confirmation of the number of dead and wounded throughout the region.
Russia, which has accused Georgia of "genocide" in South Ossetia, had provided support to the separatists and acted as a peacekeeper in the province, responded to Georgia's invasion by pouring troops and tanks south through the Caucasus mountains into South Ossetia to drive back the Georgians.
Russian troops and tanks took control of Tskhinvali, the region's devastated capital, early on Sunday after a three-day battle.
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.
However, some fighting still gripped parts of the Caucasus region and Russia demanded an unconditional Georgian withdrawal.
The conflict has 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.
Mr Cheney's office said in a statement that "the Vice-President expressed the United States' solidarity with the Georgian people and their democratically elected Government in the face of this threat to Georgia's sovereignty and territorial integrity".
It said Mr Cheney told Mr Saakashvili that "Russian aggression must not go unanswered, and that its continuation would have serious consequences for its relations with the United States, as well as the broader international community".
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, Mr 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," Mr Kouchner said.
Mr Saakashvili appeared smiling but dishevelled to meet Mr 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.
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".
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.
