A small contingent of American troops has been in Libya in recent years helping local forces combat Islamic State and al-Qaida militants, as well as protecting diplomatic facilities.
"US Africa Command will continue to monitor conditions on the ground in Libya, and assess the feasibility for renewed US military presence, as appropriate", a statement read.
The Libyan air force, which is nominally under government control, targeted an area 50km south of the capital on Saturday morning.
Khalifa Hifter, leader of the self-styled Libyan National Army, announced Thursday his offensive on the capital city of Tripoli, the seat of Libya's United Nations -backed government, leading to fresh clashes with rival militias.
The North African country has been gripped by unrest since its longtime leader, Muammar Gaddafi, was overthrown and killed in 2011.
The Libyan National Army (LNA) forces headed by Colonel Khalifa Haftar launched an air strike in southern Tripoli on Sunday, according to witnesses and various wire agencies. The airport was destroyed in a previous bout of militia fighting in 2014.
It said at least 55 fighters and a civilian were wounded.
On Thursday, LNA forces took the town of Gharyan 100km (62 miles) south of Tripoli.
Fayez Sarraj, chairman of the Presidential Council of Libya, said his government had offered concessions to Hifter "to avoid bloodshed and to end divisions" and was surprised by Hifter's order to take the capital.
Tripoli-based army spokesperson Gununu said that troops are advancing on "all frontlines" and have captured "many military vehicles" from Haftar's forces.
Rival militias, affiliated with a UN-backed government in Tripoli, said they had also carried out airstrikes, slowing Haftar's advance.
The fighting was so fierce that the United Nations called for a two-hour truce so that the injured and vulnerable civilians could be evacuated.
Ahmed al-Mesmari, spokesman for the self-styled Libyan National Army led by Hifter, said 14 troops had been killed since Hifter declared the offensive.
Various media reports say Hifter's troops have made inroads and seized control of Tripoli International Airport.
The Tripoli Protection Force, an alliance of pro-government militias in the capital, said its fighters had taken part in the recapture of the checkpoint 27 km to its south.
On April 4, Haftar announced the launch of an offensive on Tripoli.
Armed groups allied to the Tripoli government have moved more machinegun-mounted pickup trucks to defend Tripoli from Misrata down the coast.
German Foreign Minister Heiko Maas said there should be pressure on all the actors in Libya "especially general Haftar".