The operation was launched late on Tuesday and went on through the night into Wednesday.
The onslaught of anti-terrorism has given rise to gunfire, weapons fire and several explosions in an area cordoned off by the forces of law and order in the district of Isani, has found an AFP journalist on the spot. She did not say where they were from or name a specific group, according to RFE/RL's Georgian Service.
"The special operation organized by Georgia's State Security Service has completed at Gabriel Salosi Street, Tbilisi".
Giorgobiani said the suspects targeted by the operation were "foreign nationals" who are suspected of having ties with a "terrorist organization".
Georgia's state security service said that unspecified suspects opened fire on its counter-terrorist units that were conducting a special operation on the outskirts of Tbilisi.
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One was killed and four injured among the Security forces during the operation, added the official.
The building in which the suspects are located is surrounded, several police brigades control the perimeter.
"Investigation is under way both in Georgia and overseas to establish the suspects' criminal links", she said.
Special forces and vehicles are leaving the scene, APA's local bureau reported. Residents of nearby buildings were evacuated.