The assailant is probably heading for the location where a helicopter has landed, "Kurieri" news program reports.
Earlier, hostage Irakli Kvaratskhelia wrote on social media that law enforcement officers brought the armed assailant money, and all hostages, except for three, were released afterward.
"They let everyone go, except for three people. A police officer has brought money, and they will leave the building in a couple of minutes, together with the hostages. I am immensely thankful for all your support. They will probably take me for interrogation," Kvaratskhelia wrote.
A gunman broke into the Bank of Georgia in Zugdidi and took hostages. He demands half a million dollars and a helicopter.
A special operation in the municipality has been in progress for a couple of hours.