"Georgia's territorial integrity and borders must command the same respect as every other nation's, including Russia's," he said.
Bush's statement came after Russia's parliament passed resolutions calling for the recognition of South Ossetia and Abkhazia as independent states on Monday.
Both houses of the Russian parliament called on Dmitry Medvedev, Russia's president, to recognise the independence of the two regions.
The move is likely to stoke tensions between Moscow and Georgia's Western allies, who already accuse Russia of not complying with an EU-brokered ceasefire agreement to withdraw troops to pre-conflict levels in Georgia.
Earlier, the US state department said it was "unacceptable" for the Russian parliament to recognise the independence of South Ossetia and Abkhazia.
"To us that would be unacceptable... Russia needs to respect the territorial integrity and sovereignty of Georgia," said Robert Wood, a spokesman for the department.
The White House also said Dick Cheney, the US vice-president, was to visit Georgia in September as part of a regional tour that is to include Ukraine and Azerbaijan, to show US support for former Soviet states.
The Georgian foreign ministry reacted angrily to the Russian parliament's vote.
"We consider this decision another step in Russia's fight against Georgian sovereignty," Giga Bokeria, the deputy foreign minister, said.
"It is, and will be, if accepted by the Russian president, a continuation of Russian aggression against Georgia and a serious violation of international law."
But Temur Yakobashvili, the Georgian reintegration minister, dismissed the Russian move, saying it would not lead to formal recognition.
"I see no real importance, from the legal point of view, that this decision may have for the future of Abkhazia and South Ossetia," he said.
"Abkhazia and South Ossetia cannot become independent states just as a result of the Russian parliament's decision," he said.
In an interview with the French daily newspaper Liberation, Mikheil Saakashvili, Georgia's president, warned of "disastrous results" if the Kremlin officially recognised the two regions as countries.
It would be "an attempt to change Europe's borders by force", he added.
Germany urged Medvedev to ignore the parliament vote and Franco Frattini, the Italian foreign minister, called on him to be "particularly prudent" in his decision.
Al Jazeera's Nazanine Moshiri, reporting from Moscow, said that Medvedev risked creating a "domino effect" if he approved the Russian parliament's decision.
Such a move could have consequences for Russia itself and separatists in Russian regions could call for themselves to be independent too, our correspondent said.
|South Ossetia has accused Georgia of "genocide" [AFP]
Analysts say the vote gives the Kremlin an extra bargaining chip in its dealings with the West as it tries to reassert influence in the former Soviet republics and resist moves by Georgia and Ukraine to join Nato.
Currently, neither Russia nor any other member of the United Nations recognises the independence claims of South Ossetia and Abkhazia.
Both won de-facto independence in the 1990s after wars with Georgia and have survived ever since with Russia's financial, political and military support.
Russia's call for the recognition of Georgia's two breakaway regions follows the recent fighting between Russia and Georgia over South Ossetia.
Addressing the Federation council, Eduard Kokoity, the South Ossetian leader, praised the Russian intervention in the conflict, saying Russia had saved his region from "genocide" at the hands of Georgia.
He asserted there was more political and legal legitimacy to recognising South Ossetia's independence than there had been for Kosovo, the Serbian province which broke free with EU and US backing.
Sergei Bagapsh, the Abkhaz separatist leader, said "neither Abkhazia nor South Ossetia will ever again live in one state with Georgia".
Russia withdrew tanks, artillery and hundreds of troops from their most advanced positions in Georgia on Friday.
But Russian troops still control access to the port city of Poti, south of Abkhazia, and have established other checkpoints around South Ossetia.
The EU has signalled growing impatience with Russia.
Nicolas Sarkozy, the French president who helped broker a six-point ceasefire plan between Russia and Georgia to end the conflict, announced a special European summit on the Georgia crisis to be held on September 1.
Sarkozy has asked Russia to pull out its troops from western Georgia in line with the six-point plan.
Russia says the deal gives it the right to leave "peacekeepers" deep inside Georgia in a buffer zone.
Meanwhile, Medvedev said on Monday that Russia was prepared for a full break in relations with Nato but urged the Western military alliance to avert such a rupture.
"We will take any decision including up to a complete break in relations if Nato countries decide to suspend co-operation with Russia," Medvedev said during a meeting with Dmitry Rogozin, Russia's envoy to Nato.
"There has been a dramatic worsening of our relations [with Nato], but we are not to blame.
"We would like to have a full-fledged relationship and partnership, but we don't need the illusion of a partnership."
Nato last week suspended meetings of a Nato-Russia co-operation council to press demands that Moscow pull its forces out of Georgia and has called for the troops to return to positions they held before the conflict in South Ossetia.