The health ministry said 120 other people were injured in the fighting and there may be further casualties.
The battle over the airport is being waged by a powerful militia from the western city of Zintan, which controls the facility, and Islamist-led militias, including fighters from Misrata, east of Tripoli.
The clashes resumed over the weekend after ceasefire efforts failed.
Libya is going through one of its worst spasms of violence since the 2011 ousting of long-time dictator Colonel Muammar Gaddafi.
Rival militias have forced a week-long closure of petrol stations and government offices. Thousands of people have fled their homes after the fresh fighting erupted.
The violence included rocket and missile exchanges and last week saw several aircraft parked at the airport damaged. Flights have been cancelled and the airport terminal has also been damaged.