"We ask the government of Abkhazia to call on the Russian Federation ... and international organisations and the international community to start the process of recognition of an independent Republic of Abkhazia," a petition the parliament read.
Abkhazia broke away from Georgia after a war in 1992-1993 but is not recognised as an independent nation by any other country.
The resolution declared that the region had all the qualities of an independent state.
"The 13-year postwar period has confirmed the viability of the de facto independent state of Abkhazia, and the only thing that has to be done now is confirm and legitimise this sovereignty, just like it was done in relation to other countries in a similar situation," it said.
The majority of the Black Sea province's population holds Russian passports and Russia maintains a border crossing with the isolated region.
Georgia has accused Russian troops, who are based in Abkhazia as part of a peacekeeping mission, of supporting the terrorists.
Territory: 8,700 sq km
Capital city: Sukhumi (Akua in Abkhaz)
Ethnic groups: Abkhaz, Armenians, Georgians, Greeks, Megrelians, Russians, Ukrainians
Source: Unrepresented Nations and Peoples Organisation
Mikhail Saakashvili, the Georgian president, has vowed to bring Abkhazia, and another breakaway region South Ossetia, back under the control of Tbilisi.
Russian officials have said that if the Serbian province of Kosovo is granted independence, similar requests from Abkhazia, South Ossetia and Moldova's separatist Transdniestria province should also be considered.
One week ago, Transdniestria appealed to other ex-Soviet states, including Russia, to recognise its independence. Russia has not reacted to the Transdniestrian appeal.
Relations between Moscow and Tbilisi have reached a low point after Georgia arrested four Russian military officers on charges of espionage and the Kremlin retaliated by imposing a transport and postal blockade.