Several Grad rocket struck the airport late on Monday, destroying 90 percent of the planes parked there, government spokesman Ahmed Lamine said.
"The government has studied the possibility to bring international forces to enhance security," he said.
The rockets damaged the airport's control tower and two people were killed in the attack, Reuters reported.
Authorities had closed the airport due to previous fighting on Sunday, which medics say killed at least seven people .
Rival militias have clashed for control of the airport. The powerful Zintan armed group, which has been in control of the airport since the fall of Muammar Gaddafi, was still holding it by Monday.
Meanwhile, the United Nations mission in Libya said it was withdrawing its staff from Libya "temporarily" because of the deteriorating security in the country.
Tripoli has been witnessing one of its worst spasms of violence since the ouster of longtime ruler Muammar Gaddafi in 2011.
Militias, many of which originate from rebel forces that fought Gaddafi, have become powerful players in post-war Libya, filling a void left by weak police and security and cooperating with the government to provide order.
In the eastern city of Benghazi, at least six people have been killed and 25 wounded in heavy fighting between security forces and rival militias since late Sunday.