In the statement, they called for urgent action from Russia, the United Nations, the OSCE and PACE to "influence the Georgian leadership so that it renounces military force or terrorist activity as means of solving political issues."
The unrecognized republic's parliament accused Georgian authorities of escalating tensions on the border with Abkhazia, which "could have the most severe consequences for both Abkhazia and Georgia, and endanger peace and stability in the entire Caucasus."
Abkhazia's leadership earlier said its Air Force brought down an Israeli-made Georgian unmanned combat reconnaissance plane in its airspace on March 18, and accused Georgia of repeatedly violating its airspace. Tbilisi has denied the reports.
The lawmakers' statement said: "According to international law, violation of the airspace of any state by military planes can be considered an act of military aggression."
Abkhazia has stepped up its drive for independence from Georgia since Kosovo's declaration of independence more than a month ago, which has been recognized by several world powers.
Soon after Kosovo's declaration, Abkhazia and the other Georgian breakaway territory, South Ossetia, asked Russia's parliament, the United Nations and other organizations to recognize their independence.
Both Abkhazia and South Ossetia were involved in bloody conflicts with Georgia after proclaiming independence following the split-up of the Soviet Union in 1991.
The State Duma, the lower house of Russia's parliament, proposed earlier on Thursday that the government consider increasing the number of Russian peacekeepers deployed in Georgia's conflict areas.
Peacekeeping in the Georgian-Abkhaz conflict zone is carried out by collective post-Soviet CIS forces mainly staffed with Russian service personnel.
