Most of those killed are linked to a faction allied to self-styled general Khalifa Haftar.
The town's mayor, Ibrahim Zami, described some of the killings as a "slaughter".
Libya has been in turmoil since the ousting and killing of long-time ruler Muammar Gaddafi in 2011.
The two sides are attached to loose and shifting alliances based in the east and west of Libya.
A brigade from the western city of Misrata had tried to take over the Brak El-Shati airbase which they had ceded to a faction aligned with Gen Haftar's Libyan National Army (LNA), the Reuters news agency reports.
Mohamed Agliwan, a spokesman of the western Libya faction, allied to the internationally recognised government, said they had "liberated the base and destroyed all the forces inside".
The town's mayor said some aircrafts had been set ablaze.
BBC North Africa correspondent Rana Jawad reports that clashes resumed there on Thursday morning following an attempt by a rival force to take over the base.
A hospital in the area reportedly received 60 bodies, including civilians who were working at the air base.
The death toll could not be independently verified but officials say most of those killed were fighters allied to the LNA, our reporter says.
An informal truce had been reached this month over the matter, after Gen Haftar met Fayez al-Sarraj, the UN-backed prime minister.
A meeting between the two just weeks ago had created hopes of a wider political and military settlement in the country.
At least 60 people have reportedly been killed after an attack on a military base in southern Libya following clashes between rival factions.