The search for people living in the building is underway but exact information on the possible number of victims is not yet available, the broadcaster added.
The head of the Adjara region's government Tornike Rizhvadze and Adjara's regional Health Minister Nino Nizharadze have arrived at the scene. They have promised to make a statement after reviewing the situation.
For safety reasons, rescuers evacuated the rest of the house.
The entrance of a five-story residential building in the Georgian coastal resort town of Batumi. The cause of the collapse remains unknown.