"The sooner Georgia joins NATO, the sooner our independence will be recognized," Nugzar Ashuba said.
His comments came days after a Russian lower house statement that recommended Moscow speed up the recognition of Abkhazia and another Georgian de facto independent republic, South Ossetia, in the event of NATO beginning the process of accepting Tbilisi as a member of the military alliance.
Ashuba welcomed the Russian MPs' statement. "This is another step toward the recognition of our country's independence," he said.
Shortly after Kosovo declared its independence on February 17, Abkhazia and South Ossetia, along with Moldova's Transdnestr, asked Russia's parliament, the United Nations and other organizations to recognize their independence.
Georgia has sought NATO membership ever since President Saakashvili came to power in 2003. Seventy-seven percent of Georgians are in favor of the former Soviet republic joining NATO, according to the results of a national referendum held on the issue earlier this year.
On February 14, Georgia handed a letter to NATO from President Mikheil Saakashvili asking for the country to be accepted into the Western military alliance's membership plan.
The Abkhaz parliamentary speaker also said Monday that his countrymen were ready to take up arms to defend Abkhazia from any hostile forces.
"We are not afraid of anyone - not NATO, or anyone else. If we need to defend our homeland we will do so," Nugzar Ashuba said, just days after lawmakers in Abkhazia had signed a statement accusing Tbilisi of military aggression, and warning that war could break out in the Caucasus.
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."
Abkhazia's leadership earlier said its Air Force brought down an Israeli-made Georgian unmanned combat reconnaissance plane over its territory on March 18, and accused Georgia of repeatedly violating its airspace. Tbilisi has denied the reports.
In their statement on Friday, Russian MPs also said it was necessary to protect people in Abkhazia and South Ossetia, most of whom are Russian passport holders, from a possible invasion by Georgia.
The statement also called for a strengthening of the peacekeeping force in the conflict zones between Georgia and its breakaway territories.
Peacekeeping in the Georgian-Abkhaz conflict zone is currently carried out by collective CIS forces staffed with Russian service personnel. The situation in the Georgian-South Ossetian conflict area is controlled by joint forces, also including Russian peacekeepers.
Ashuba also stated that Tbilisi would not be able to unilaterally oust peacekeepers from the conflict zones, sating that "Georgia's unilateral desire to remove Russian peacekeepers from the Georgian-Abkhaz conflict zone is clearly not enough," he said.
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.