Militiamen from the al-Awfia brigade entered the airport with tanks and armoured vehicles and occupied the runway, forcing flights to be diverted.
It is unclear if the group’s commander has been kidnapped or is being held for questioning by the government.
The group is refusing to leave until its demands are met.
The BBC reports that at least two dozen armed militiamen are at the scene.
The brigade has placed a pick-up truck mounted with an anti-aircraft gun underneath each of the six planes on the tarmac, the BBC reports.
The situation at the airport was chaotic, although not overtly dangerous at the moment, with reports that the brigade are in negotiations with security officials.
“They are on the runway, in the car park, everywhere,” an official told Reuters.
A representative from the brigade’s hometown of Tarhouna in western Libya was said to be negotiating with the rebels to convince them to give up their action.
Airport sources told the BBC that at least three airlines have cancelled their flights.