"The United States of America stands with the democratically-elected government of Georgia, [and] insists that the sovereignty and territorial integrity of Georgia be respected," he said.
He added that he expected Russia's armed forces not to hinder the US military's efforts to deliver aid.
'US must choose'
Russia denied its forces had broken a shaky ceasefire agreement brokered by France after five days of bitter fighting and Sergei Lavrov, the Russian foreign minister, said the US had to choose between its relations with Moscow and its backing of the Georgian government.
"The Georgian leadership is a special project for the United States," Lavrov said.
"At some time it will be necessary to choose between the prestige of this relatively virtual project and partnership on questions that require collective action."
Wednesday's tough talk between the former Cold War foes came amid accusations by Georgia that Russian forces had bombed and looted the town of Gori, a charge that Moscow denied.
Russia also destroyed several vessels in the Georgian port of Poti and an armoured Russian convey drove towards Tbilisi before halting just an hour's drive from the capital and camping for the night, Al Jazeera's correspondents on the ground reported.
Condoleezza Rice, the US secretary of state, is set to arrive in Tbilisi on Thursday to underline US support for the Georgian government.
Before leaving for Georgia, Rice said reports of Russian violations of the ceasefire would "only serve to deepen the isolation into which Russia is moving."
It would also "deepen the very strong, growing sense that Russia is not behaving like the kind of international partner that it has said that it wants to be," she said.
However, the Pentagon denied a suggestion by Mikheil Saakashvili, the Georgian president, that the US military would take control of the country's seaports and airports.
Geoff Morrell, a Pentagon press secretary, said on Wednesday that "we do not need nor do we intend to take over any air or seaports in order to deliver humanitarian assistance to those caught in this conflict".
"It is simply not a requirement of this mission and it is not something we are seeking to do."
|Georgian civilians have been caught up
in the fighting [EPA]
The US president also said on Wednesday that he had spoken to Nicolas Sarkozy, the French president, and the Georgian president amid a peace push by Paris, which holds the rotating European Union presidency.
The president, who had spent the morning in the White House "situation room" discussing the crisis with US officials, said "the United States strongly supports France's efforts".
He said Rice would meet Sarkozy before heading to Tbilisi, to "personally convey America's unwavering support for Georgia's democratic government".
"She will continue our efforts to rally the free world in the defence of a free Georgia," he said.
Bush also warned that US support for Russian entry "into the diplomatic, political, economic, and security structures of the 21st century" was "at risk" over Moscow's actions in Georgia.