The appeal came after Russia lifted trade restrictions on the de facto independent republic on Thursday in a move that has further strained relations with Georgia.
"The unrecognized republic has established itself as an independent, democratic state," the authors of the statement said, adding that the recognition of Kosovo by the U.S. and the majority of European countries in mid-February had irrevocably altered the geopolitical situation.
Appealing to the UN, lawmakers said the recognition of Abkhazia would contribute to peace in the region. It also said that the UN's failure to recognize Abkhazia had only served to "encourage" Tbilisi's "aggression" toward the republic.
South Ossetia, the other breakaway republic on Georgian territory, made a similar appeal for recognition to Russia on Thursday, also citing Kosovo as a factor in its bid. North Ossetia, which is part of Russia, backed the appeal.
Abkhazia and South Ossetia, with populations of about 200,000 and 100,000 respectively, were involved in bloody conflicts with Georgia after proclaiming independence following the split up of the Soviet Union in 1991.
Georgia, which has sought to regain control over the separatist republics, called Russia's decision to lift economic sanctions against Abkhazia "a blunt attempt to violate its sovereignty and territorial integrity." It also threatened retaliatory measures to protect its interests. On Friday, it summoned the Russian ambassador to Georgia to register a protest over Moscow's actions.
Moscow has repeatedly said the recognition of Kosovo will set a precedent for other breakaway regions, including in the former Soviet Union. Russia's lower house of parliament, the State Duma, is to discuss Abkhazia and South Ossetia on March 13.
Justifying its decision on Thursday, Russia cited "a change of circumstances" and blamed Georgia for a "non-constructive" policy toward Abkhazia. Moscow said preserving the sanctions no longer made sense and "is harmful for the region's socio-economic development."
Russia also called on the CIS, an alliance of post-Soviet states, to follow suit in relation to sanctions against Abkhazia.
Analysts said the Kremlin's decision to restore trade ties with Abkhazia was partially prompted by plans to use the neighboring Black Sea region's resources to build an Olympic infrastructure in the resort of Sochi for the 2014 Winter Games. Russia will also now not have to justify acquisitions of land and property in Abkhazia.
