Both houses of Russia's parliament voted unanimously on Monday in favor of a resolution asking President Dmitry Medvedev to recognize the independence of Abkhazia and South Ossetia, following requests from the leaders of both breakaway republics.
Bush said in a statement from his ranch in Texas, "I call on Russia's leadership to meet its commitments and not recognize these separatist regions."
"Georgia's territorial integrity and borders must command the same respect as every other nation's, including Russia's," he said.
Medvedev has yet to respond to parliament's request, but earlier said that South Ossetians and Abkhazians should be given a say in their status. Russian officials have said Georgia lost its right to the two regions after launching a military offensive that devastated South Ossetia.
Bush said recognition of the regions would be "inconsistent with unanimously approved United Nations Security Resolutions that Russia has consistently voted for in the past."
White House spokesman Tony Fratto told reporters on Monday that Dick Cheney would visit Georgia in early September.
"The Vice President will be delivering... the word of America's support, and also consulting on how these leaders in the region see the future playing out," he said.
The trip, starting on September 2, will also include Ukraine, another post-Soviet country with NATO ambitions, as well as Azerbaijan and Italy.
NATO has said that despite the conflict between Russia and Georgia, the South Caucasus country remains on course for eventual membership. The military alliance has frozen ties with Russia.
However, President Medvedev said on Monday that a rift with NATO would harm the alliance more than it would harm Russia.
The South Ossetia conflict broke out on August 8, with Georgia's artillery bombardment of regional capital Tskhinvali, which killed large numbers of civilians, mainly Russian nationals.
Russia, which retaliated with a major 'peace enforcement' operation, retains peacekeepers in South Ossetia and in a buffer zone between the province and Abkhazia, inside Georgia proper.
While Tbilisi and Western powers say that by retaining troops in Georgia Russia is in breach of a peace deal brokered by French President Nicolas Sarkozy in Moscow, Russia says the six-point agreement allows it to take "additional security measures" in Georgia.
