Abkhazia used the Ossetia conflict to drive out remaining Georgian troops
Russia's parliament has backed a motion urging the president to recognise the independence of Georgia's breakaway regions of Abkhazia and South Ossetia.
Both houses voted unanimously in favour of the non-binding motion, which analysts say could help President Dmitry Medvedev in talks with the West.
The US said any move to recognise independence of the two regions would be contrary to international law.
Russia and Georgia fought a brief war this month over the two provinces.
Moscow launched a counter-attack after Tbilisi tried to retake South Ossetia by military force.
The US and a number of Western governments have backed Georgia, sending aid and issuing strongly-worded statements.
Responding to the parliamentary vote, the US state department said recognition of the two provinces' independence would be "a violation of Georgian territorial integrity" and "inconsistent with international law".
President George W Bush said he was deeply concerned, adding: "I call on Russia's leadership to meet its commitments and not recognise these separatist regions."
Leaders from Germany, the UK and Italy also expressed concern that the vote would raise tensions further in the Caucasus.
On Monday the White House announced Vice-President Dick Cheney would visit Tbilisi next month and hold talks with President Mikhail Saakashvili, in a move analysts say will further irritate the Kremlin.
Both regions have had de facto independence since breaking away in the early 1990s.
While they have enjoyed Russian economic and diplomatic support, and military protection, no foreign state has yet recognised them as independent states.
Meanwhile, Moscow has stepped up its rhetoric on the issue.
Mr Medvedev said Russia could deal with anything Nato could threaten it with - including the severing of all ties.
And Prime Minister Vladimir Putin said Russia would consider scrapping some of the trade deals it had made in trying to gain entry to the World Trade Organization (WTO).
On the ground, most of Russia's forces pulled out of Georgia last Friday.
But some troops continue to operate near the Black Sea port of Poti, south of Abkhazia, where Russia says it will carry out regular inspections of cargo, fuelling speculation that Moscow is imposing an economic stranglehold on Georgia.
Troops also continue to operate in buffer zones that Russia controversially set up within undisputed Georgian territory.
France's President Nicolas Sarkozy said at the weekend that, under the terms of the ceasefire he had helped broker, troops from the Organization for Security and Co-operation in Europe (OSCE) would move into these buffer zones.
But senior Russian officials now say they never agreed to allow international peacekeepers to patrol in the zones, and also say they will not allow aerial reconnaissance over the zones.
The upper house, Federation Council, voted 130-0 to call on President Medvedev to support the independence of Abkhazia and South Ossetia.
The lower house, the State Duma, approved the same resolution in a 447-0 vote shortly afterwards.
South Ossetians rallied for independence last week
The Federation Council speaker, Sergei Mironov, said both Abkhazia and South Ossetia had all the necessary attributes of independent states.
During the debate in the two chambers, several speakers compared Georgia's military action in South Ossetia with Hitler's World War II invasion of the Soviet Union.
Both Abkhaz leader Sergei Bagapsh and his South Ossetian counterpart, Eduard Kokoity, addressed the Russian lawmakers before the votes, urging them to recognise the independence of the two regions.
"It's a historic day for Abkhazia... and South Ossetia," Mr Bagapsh said, adding that Abkhazia would never again be part of Georgia.
Mr Kokoity thanked Russia for supporting South Ossetia during the conflict with Georgia, describing President Medvedev's move to deploy troops as "a courageous, timely and correct" decision.
He said that South Ossetia and Abkhazia had more rights to become recognised nations than Kosovo, which declared independence from Serbia earlier this year with support from the US and much of the European Union.
Both houses of the Russian parliament are dominated by allies of Mr Medvedev and Mr Putin.
The lawmakers interrupted their summer holidays for extraordinary sittings, formally called at the request of separatist leaders in the two Georgian provinces.
In a televised address, President Saakashvili dismissed the vote, saying: "Nobody can legalise the annexation of the Georgian territories."
While both Abkhazia and South Ossetia have been pushing for formal independence since the break-up of the Soviet Union in the 1990s, Russia's official line at least until now has been similar to that of the West, the BBC's Humphrey Hawksley reports from Moscow.
But in March the State Duma passed a resolution supporting independence should Georgia invade or rush to join Nato.
After Monday's votes, the bill will be sent to the Kremlin for approval.
Analysts say the Kremlin might delay its decision while it carries out wider negotiations with the West on the crisis.