The United National Movement of President Mikheil Saakashvili, which has dominated parliament for eight years, is set to move into the opposition with the remaining 67 seats.
Election officials say the figures have yet to be finalized while courts examine cases of alleged rigging.
Georgian Dream is also contesting seven seats, which could leave it holding a total of 90.
The outright majority leaves Georgian Dream placed to approve, unopposed, its nominee for a prime minister, who will hold the bulk of political power according to constitutional amendments going into effect next year.
Georgian Dream's leader, billionaire Bidzina Ivanishvili, has expressed an intention to serve as prime minister.