The week-long fight 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 early Sunday after cease-fire efforts failed.
A security official said the fighting killed two militiamen from Misrata and a civilian who died when a stray rocket hit his house.
The official spoke on condition of anonymity because he was not authorized to speak to journalists.
A mortar shell struck a Libyan Arab Airlines plane and a column of black smoke could be seen billowing from inside the airport, which has been closed since Monday.
Tripoli is witnessing one of its worst spasms of violence since the ouster of longtime dictator Moammar Gadhafi in 2011. The rival militias, made up largely of former rebels, have forced a week-long closure of gas stations and government offices.
In recent days, armed men have attacked vehicles carrying money from the Central Bank to local banks, forcing their closure. The Central Bank had said banks would reopen Sunday, but they remained closed as the fighting resumed.
Renegade former army officer Khalifa Hafter, who is waging his own offensive against Islamic militants in the eastern city of Benghazi, denounced what he called an attempt by “remnants and agents of terrorism” to destroy Tripoli’s airport and terrorize the people.
Hafter, who appeared Saturday on Libyan television, said: “Our troops in Tripoli have bravely confronted the aggressive militia attacks” and vowed that the “coming few days will be decisive with the escalation of our military operations.”
In Benghazi, Libya’s second-largest city, gunmen killed an army officer late Saturday while he was driving home in his car, and early Sunday a former special forces officer was shot dead in the downtown Salmani district, a local security official said. The official spoke on condition of anonymity because he was not authorized to brief reporters.
The United Nations Support Mission in Libya said last week it was temporarily withdrawing its staff because of the deteriorating security situation.