The chairman of the parliament's Defense and Security Committee, Givi Targamadze, said the move was caused by "a rise in threats facing Georgia," adding that it was an "appropriate response aimed at strengthening the country's military capability."
Opposition party members have also given their support for the bill.
Relations between Russia and Georgia plunged to a new low recently against the backdrop of outbreaks of violence in Abkhazia and South Ossetia, with the two countries trading accusations of provoking violence.
Last week, Russian military aircraft flew over South Ossetia. Moscow said it wanted to monitor the situation in the region due to fears that Georgia would invade the internationally unrecognized but de facto independent republic. Tbilisi called the flights an act of "military aggression" against Georgia and recalled its ambassador from Moscow.
Russia recently deployed additional peacekeeping troops to Abkhazia.
Talking about the troop increase, Targamadze said that Georgia also needed to increase its armed forces as it had expanded its participation in the international military operations. Last year, Georgia increased its military personnel from 20,000 to 32,000.
The tiny Caucasus state is seeking to be admitted to a NATO Membership Action Plan in December, which would pave the way for entry into the military bloc. The ambition has added to tension in relations with Moscow.
The Georgian parliament also voted on Tuesday to increase the country's military budget by an additional $210 million by the end of the year, taking the total military spending for 2008 to $997 million.
