He also said he was sending Condoleezza Rice, the US secretary of state, to Tbilisi, the Georgian capital, to show his support for the Georgian government.
Standing alongside Rice and Robert Gates, the US defence secretary, Bush warned Moscow against breaking its pledge to halt its military action and announced that a US humanitarian aid flight was already on its way to Georgia.
However the Pentagon later denied a suggestion by Mikheil Saakashvili, the Georgian president, that the US military would take control of the country's seaports and airports.
"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," Geoff Morrell, a Pentagon press secretary, said on Wednesday.
"It is simply not a requirement of this mission and it is not something we are seeking to do."
Sergei Lavrov, the Russian foreign minister later said the US had to choose between it 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."
The US president also said 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.
|Georgian civilians have been caught up
in the fighting [EPA]
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.
He said: "To begin to repair the damage to its relations with the United States, Europe, and other nations, and to begin restoring its place in the world, Russia must keep its word and act to end this crisis."
Bush also called on Moscow to abide by the EU-mediated ceasefire agreed a day earlier and to withdraw its military forces from Georgia.
"We expect Russia to meet its commitment to cease all military activities in Georgia, and we expect all Russian forces that have entered Georgia in recent days to withdraw from that country," he said.
He said he had reports of Russian actions "inconsistent" with Moscow's statements that it has halted military operations and agreed to a provisional ceasefire.