The self-styled Libyan National Army, led by Khalifa Hifter who last week launched the push on Tripoli, acknowledged striking the Mitiga airport, barely 8 kilometers (5 miles) east of the city center.
Hifter's forces have clashed with rival militias which support the U.N.-backed government that controls Tripoli and the western part of the country. The escalation has threatened to plunge the fractured North African nation deeper into chaos and ignite civil war on the scale of the 2011 uprising that toppled and killed longtime dictator Moammar Gadhafi.
The U.N. said the latest fighting has displaced some 3,400 people and blocked emergency services from reaching casualties and civilians.
The World Health Organization said two doctors were killed trying to "evacuate wounded patients from conflict areas."
Ibrahim Fadel, an official at Mitiga, said no casualties were reported in the airport attack. Flights were suspended for several hours but the airport reopened later Monday and said it would resume operations going forward from 7 a.m. till 7 p.m.
The official Facebook page of Mitiga, run by the U.N.-backed government, said a fighter jet attacked the facility but gave no other details. A video circulated online shows a fighter jet firing and apparently targeting the airport, formerly a military base.
Maj. Gen. Mohamed al-Manfour of Hifter's Libyan National Army, told the Libyan Address newspaper they bombed targets at Mitiga after receiving information that the U.N.-backed government forces were preparing to target them.
U.N. spokesman Stephane Dujarric told reporters in New York on Monday that "unfortunately" the United Nations received "no positive news" in response to its urgent appeal for a truce in Tripoli. A cease-fire is imperative to ensure that civilians trapped in fighting around the Libyan capital can escape to safer areas and that the wounded can be evacuated, he said.
The U.N. humanitarian coordinator in Libya, Maria do Valle Ribeiro, said the clashes have also worsened the situation for migrants held in detention centers in Tripoli, she warned.
Meanwhile, fighting was underway Monday at Tripoli's former international airport, some 24 kilometers (15 miles) south of the city. That airport was closed in 2014 after fighting destroyed much of it.
Ahmed Musbah, a resident who lives near the area, said he could hear shooting coming from the direction of the town of Bin Ghashir, to the south. "The sound of fighting seems to be closing in," he said.
Hifter's forces said Saturday they had seized the old airport. However, militias supporting the U.N.-backed government in Tripoli claimed Monday they recaptured the facility.
The Health Ministry of the Tripoli-based government said at least 27 people, including civilians, were killed and at least 27 wounded since the start of Hifter's offensive against the capital. The media office of Hifter's army said 22 of their troops had been killed since Thursday.
It was not immediately clear when the two doctors whose deaths were reported by the WHO were killed in Tripoli.
Ahmed Al Mandhari, WHO's director for the eastern Mediterranean, said that targeting of medical staff was "unacceptable" and "worsens the situation for civilians caught up in conflict."
The European Union's foreign policy chief, Federica Mogherini, called on the warring sides to stop fighting and start talking.
Speaking at the EU's foreign ministers meeting in Luxembourg, Mogherini said all sides in the recent surge in fighting should "go back to the negotiating table under the auspices of the U.N."
Also Monday, U.N. envoy Ghassan Salame said he met with Fayez Sarraj, head of the government in Tripoli, to discuss how the U.N. mission "can assist at this critical and difficult juncture."
Salame later Monday condemned the attack on Mitiga, saying it was "a serious violation of international humanitarian law."
He has asked for "an immediate halt to any further air operations" in order to bring the country back from the brink of what he called "the effective start of a civil war."
Salame has said he is still planning for the April 14-16 National Conference aimed at bringing all Libyan factions together to chart a course to elections.
"We need all the parties involved in this conflict to attend," Dujarric said.
Since Gahdafi's ouster, Libya has been governed by rival authorities in the east and in Tripoli, in the west, each backed by various militias and armed groups fighting over resources and territory.
In Cairo, Agila Saleh, head of Libya's east-based parliament, backed Hifter's offensive and the Libya National Army, saying that militias have been "hijacking" the capital.
"The Libyan army moved towards Tripoli with one goal, to free Tripoli from armed militias," he said after meeting with the Arab League's secretary-general, Ahmed Aboul Gheit.
On Sunday, Marine Corps Gen. Thomas Waldhauser, the head of U.S. Africa Command said the United States has temporarily withdrawn some of its forces from Libya due to "security conditions on the ground."
A small contingent of American troops has been in Libya in recent years, helping local forces combat the Islamic State group and al-Qaida militants, as well as protecting diplomatic facilities.