In a statement, Medvedev blamed Georgian president Mikhail Saakashvili for the crisis.
The Georgian government "made its choice in the early hours of August 8th," he said, referring to the day Georgia began a military operation against separatists in South Ossetia, which led to a Russian retaliation to support the South Ossetians. "Saakashvili has thus killed every hope for peaceful coexistence of Ossetians, Abkhazians and Georgians within one country."
But many in the West see Russia's actions as a return to Soviet-style intervention in nearby countries' affairs. After a five-day war, Russian troops have remained in South Ossetia, manning checkpoints in what the Russians are calling "security zones."
Reaction by Western leaders allied with Georgia was swift.
U.S. Secretary of State Condoleezza Rice said the bid to recognize the two regions would be "dead on arrival" at the United Nations.
"Abkhazia and South Ossetia are a part of the internationally recognized borders of Georgia and it's going to remain so," she said in a statement from the West Bank, where she is travelling.
The head of Europe's human rights and security body, the Organization for Security and Cooperation in Europe (OSCE) also decried the move.
"The recognition of independence for South Ossetia and Abkhazia violates fundamental OSCE principles" OSCE chairman Alexander Stubb said.
Meanwhile, residents celebrated in the streets in Sukhumi, the capital of Abkhazia, and Tskhinvali, the capital of South Ossetia.
"We feel happy. We all have tears in our eyes. We feel pride for our people," 38-year-old lawyer Aida Gubaz of Sukhumi told Reuters. "Everything we went through, now we our getting our reward."
In Tskhinvali about 500 people had gathered in the central square, and celebratory gunfire could be heard throughout the city, Reuters reported.
Meanwhile, the crisis has highlighted tensions between Russia and the U.S.
On Sunday the U.S. sent the missile destroyer USS McFaul to the southern Georgian port of Batumi to deliver humanitarian aid. The ship left Tuesday but will remain in the Black Sea area, a U.S. Navy spokesman told the Associated Press. The U.S. Coast Guard Cutter Dallas is headed to Poti -- a port city where Russian soldiers are still manning a security checkpoint -- with aid.
Col. Anatoly Nogovitsyn, deputy head of the Russian military's general staff, said that Russia was worried about the U.S. naval operation and called it "devilish."
