The EU has frozen Georgia’s membership bid because of “democratic backsliding” only months after official membership talks last December.
Polling has put Georgian Dream on course to win around a third of the vote.
Turnout was at its highest since the last transfer of power 12 years ago, according to political intelligence firm Europe Elects.
Around 3.5 million Georgians are eligible to vote before polls close at 4pm local time.
Salome Zourabichvili, the Georgian president and critic of Georgian Dream, said in remarks to the nation on Saturday: “It is crucial for this momentum to continue through the second half of the day, and we anticipate even greater participation.”
Ms Zourabichvili stated there had already been disruption of the vote, seemingly confirming fears of violence that had been raised in the build-up to the landmark election.