But Russian Prime Minister Vladimir Putin accused Western states of turning a blind eye to alleged atrocities by Georgia's forces during their surprise offensive last week.
Georgian President Mikhail Saakashvili, who described Russia as a "barbaric aggressor" in a speech on Georgian TV, has accused Russia of "expelling" ethnic Georgians from both breakaway regions.
Speaking later to the BBC in Tbilisi, after a brief visit to the town of Gori near South Ossetia as it was being evacuated, he said Russia had been preparing to attack Georgia for months.
He said his country had been split in two.
Mikhail Saakashvili on the escalating conflict with Russia
Fighting erupted last Thursday night when Georgia sent its army to regain control of South Ossetia which, like Abkhazia, has had de facto independence since the early 1990s, with Russian backing.
Russia poured armour and troops into the region, ejecting the Georgians, and now appears to control many key bridges and roads across the country.
The UN Security Council in New York discussed a draft resolution on an immediate ceasefire but it failed to gain agreement.
French President Nicolas Sarkozy will continue the diplomatic moves on Tuesday when he holds talks in both Moscow and Georgia.
'Dramatic and brutal'
Speaking moments after he arrived back in the US from the Beijing Olympics, President Bush said he was deeply concerned about reports of Russian intentions.
US President George W Bush statement on Georgia
He said he had seen reports that Russia might soon attack the Georgian capital, Tbilisi, which would, he said, represent a "dramatic and brutal escalation" of the conflict.
"Russia's government must respect Georgia's territorial integrity and sovereignty," he said.
"The Russian government must reverse the course it appears to be on."
Russia's actions, Mr Bush added, were "jeopardising" its relations with the US and EU.
He urged Moscow to accept an EU-brokered peace agreement that Mr Saakashvili has already signed.
This was the strongest statement yet from President Bush and appeared to be aimed at drawing a line in the sand, preventing Russia from overthrowing the Georgian government, the BBC's Justin Webb reports from Washington.
Speaking in Moscow, Mr Putin questioned the moral support "some" states were extending to Georgia's leaders, saying they were trying to "portray victims of aggression as aggressors".
The late Iraqi leader Saddam Hussein, he said, had been hanged for "destroying several Shia villages".
But Georgia's current leaders, he alleged, had "razed 10 Ossetian villages at once", killing civilians indiscriminately.
Russia's announcement of its raid on Senaki was the first confirmation that it had advanced beyond the borders of Abkhazia.
Our visits to these hospitals confirm that local medical facilities are dealing with a large number of wounded and dead
But Dominik Stillhart, the organisation's deputy director of operations, did say that visits to several hospitals in Georgia and on Russian territory had confirmed that "we are dealing with a large number of wounded and dead".
In other developments:
• Georgia's foreign minister is due to meet Nato officials on Tuesday. Russia has also requested an emergency meeting with Nato, saying the organisation should hear Moscow's side before making any decisions
• The US and several European nations have begun to evacuate hundreds of their citizens from Georgia
• Estonia, Latvia, Lithuania and Poland issue a joint statement saying that as "once-captive nations of Eastern Europe" they share a "deep concern" about Russia's actions towards Georgia
• The G7 group of developed countries issues a strongly-worded statement calling on Russia to accept the EU-brokered ceasefire agreement
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