The attackers have demanded half a million dollars, an unarmed negotiator and security guarantees.
Moreover, they have given police a deadline of two hours for special forces to be removed from the perimeter, says Mtavari Arkhi.
The attackers say there are 19 hostages in the building.
TV channel Formula published information that one of the hostages said there are three attackers in total.
One of the released employees, Ana Shonia, who made her way outside to freedom with the help of a bank customer, says some people were released by the attacker.
The Georgian Ministry of Internal Affairs received a report about the case at 14:21.
A Bank of Georgia branch in the west Georgian city of Zugdidi has been taken hostage by robbers.
Witnesses have reported gunshots. So far, no injuries have been reported.
Special forces units are outside the building.
One of the employees who was able to make their way out of the building said one individual shot several times and asked employees to get down on their knees.
Several individuals have been spotted on the roof of the building
The bank is located on On Zviad Gamsakhurdia Avenue in Zugdidi, and the area has been cordoned off.
Additional details will follow as developments unfold.