With 12 % of the vote counted, the main opposition bloc, United Opposition, is in second place with 15.42%, according to the Central Election Commission.
An exit poll carried out by QEV Analytics, the Jaan Tonosson Institute, and the Ukrainian Initiative Fund said on Wednesday that the ruling party had gained 63.2% in the elections.
The opposition, which met in the capital, Tbilisi, for a late night protest after voting had finished, has promised to start a "people's rebellion" if they suspect the elections of being rigged.
Voting was not held in the country's two breakaway republics of Abkhazia and South Ossetia, the cause of recent rising tensions with Russia.
These are the seventh parliamentary elections to be held in Georgia since it proclaimed independence in 1991. The country last held parliamentary polls in March 2004.
