The votes by both chambers of Russia's parliament, which were not legally binding, come as the White House announced Vice President Dick Cheney would travel to three former Soviet republics next week - Georgia, Ukraine and Azerbaijan.
"Russia's historic role of the guarantor of peace in the Caucasus has increased," said Boris Gryzlov, speaker of the lower chamber. "The Caucasus has always been and will remain the zone of Russia's strategic interests."
Reaction from the West was swift. The United States said Russian recognition of South Ossetia and Abkhazia "would be unacceptable."
"Russia needs to respect the territorial integrity of Georgia," said State Department spokesman Robert Wood.
The continued presence of Russian troops in Georgia after a lightning war over the separatist regions of South Ossetia and Abkhazia has sunk relations between Russia and the West to a post-Cold War low. Western nations have accused Russia of reneging on its commitment to withdraw forces from U.S.-allied Georgia.
The European Union immediately declared after the Russian vote that South Ossetia and Abkhazia should remain in Georgia. German Chancellor Angela Merkel said recognizing the two separatist provinces would create a "very difficult, critical situation" in regard to Georgia's territorial integrity.
The vice president's office described Cheney's trip, which begins Sept. 2 and also includes a stop in Italy, where the U.S. has a major base, only in the broadest terms, saying President Bush wants his No. 2 to consult with key partners on matters of mutual interest.
Experts say the Russian parliament's blessing of the Georgian separatists gives the Kremlin extra leverage as Russia tries to reassert its influence in the former Soviet republics and resist moves by Georgia and Ukraine to join NATO.
Currently, neither Russia nor any other U.N. member recognizes the two provinces' independence claims. Both won de-facto independence in the 1990s after wars with Georgia, and have survived since with Russia's financial, political and military support.
"Neither Abkhazia ... nor South Ossetia will be part of the Georgian state," Abkhazian leader Sergei Bagapsh told the upper chamber of Russia's parliament Monday.
Despite their desire for independence, one or both regions could eventually be absorbed into Russia.
"Ossetians have no doubts - we'll only be with Russia," said Robert Bestayev, 36, a beaming South Ossetian military communications officer in Tskhinvali, the provincial capital.
Russia's critics say the conflict in Georgia heralds a new, worrying era in which an increasingly assertive Kremlin has shown itself ready to resort to military force outside its borders.
After Georgia tried to reassert control of South Ossetia by force Aug. 7, Russian troops overwhelmed the Georgians, and for nearly two weeks occupied positions deep within Georgia. Most Russian forces withdrew Friday, although some troops continue to operate near the Black Sea port of Poti and just outside the boundaries of the breakaway regions.
French President Nicolas Sarkozy has called a special meeting of EU leaders Sept. 1 to discuss aid to Georgia and future relations with Russia. France holds the 27-member bloc's rotating presidency. French Foreign Minister Bernard Kouchner, however, said Monday the EU was not considering any sanctions against Moscow.
Ukraine, like Georgia, has angered Moscow by courting the West and seeking NATO membership. President Viktor Yushchenko said last week that the Russian offensive demonstrated that joining NATO is the only way Ukraine can ensure its security.
In a show staged for Russian eyes, Ukraine paraded tanks and other military hardware during Independence Day celebrations Sunday for the first time since 2001.
Russian President Dmitry Medvedev signaled for calm in the face of Western criticism. NATO has suspended operations of its vehicle for cooperation with Russia over the Georgia crisis, but Medvedev said Monday there would be "nothing frightening" for Russia if the alliance were to sever ties altogether.
On Sunday, a U.S. Navy destroyer loaded with humanitarian aid reached Georgia's Black Sea port of Batumi, bringing baby food, milk, bottled water and a message of support for an embattled ally.
The guided missile cruiser, carrying about 55 tons of humanitarian aid, was the first of three American ships scheduled to arrive this week.
But the deputy chief of Russia's general staff suggested Monday the arrival of U.S. and other NATO warships in the Black Sea would only increase tensions. Russia shares the sea with NATO members Turkey, Romania and Bulgaria, as well as Georgia and Ukraine.
The South Ossetian government, meanwhile, accused Georgian forces of taking control of three villages on the edge of the breakaway region Monday after Russian troops withdrew. Acting Prime Minister Boris Chochiyev said a delegation was dispatched for negotiations.
"We are hoping to resolve this situation peacefully. And if that doesn't work out, there are other methods," he said.
Georgian Interior Ministry official Shota Utiashvili said Georgian police were in the villages, not soldiers. He said the villages were under Georgian control before the fighting began Aug. 7, and under the EU-brokered cease-fire Georgia has the right to station police there.
"We haven't seized anything," he said.
Meanwhile, President George W. Bush says Medvedev should not recognize the breakaway regions of Georgia as independent countries despite pleas from Russian lawmakers.
Bush put out a statement criticizing Russia's parliament. The White House says those two regions, South Ossetia and Abkhazia, remain part of Georgian domain.
Bush said Russia's leadership should "not recognize these separatist regions."
He said Georgia's borders deserve the same respect as any country's - including Russia's.