An air strike on the southern part of Tripoli was confirmed by a witness who spoke to Reuters.
The rival militias, which are affiliated with a UN-backed government in Tripoli, said they had also carried out airstrikes, slowing Hifter's advance.
The U.N. mission to Libya (UNSMIL) called on Sunday for a truce for two hours in southern Tripoli to evacuate civilians and wounded, it said in a statement without giving details.
Libya remains torn by a prolonged civil war since 2011 when its longtime leader Muammar Gaddafi was toppled and killed during a US-led military intervention.
In a televised address, Sarraj warned of a "war without a winner".
The air strikes came as fresh fighting flared Saturday south of Tripoli between the pro-government forces and Haftar's troops despite calls from the global community to halt the military offensive. It is the first public mention that America had troops on Libyan soil.
Forces loyal to Libya's UN-backed unity government arrive in Tajura, a coastal suburb of the capital Tripoli, on Saturday. But gaining control of Tripoli - the ultimate prize for Haftar's eastern parallel government - would be far more complicated. UN's chief Antonio Guterres, who visited both Tripoli and Tobruk this week, called on both sides to "avoid bloody confrontation".
He did not provide details on the number of USA troops that have been withdrawn or on how many remain inside the country.
He described the general's army as outlaws, adding that the armed forces of the UN-backed government of Prime Minister Fayez Sarraj would stand up to anyone trying to militarise Libya.
The UN Envoy for Libya, Ghassan Salame, speaks during a news conference in Tripoli, Libya, April 6, 2019.
There was no immediate statement from the United Nations -backed government, the militias that support it, or the United Nations.
A similar stance was taken by the UN Security Council which, following a closed-door emergency meeting Friday, said those responsible for re-igniting the conflict will be held responsible. Pro-government militias from the nearby base of Misrata have been moving to defend Tripoli.
The country's oil installations should not be used by any group for political gain, it said.
United Nations envoy Ghassan Salame said on Saturday that the conference planned for 14-16 April would still be held in time, despite the escalation - "unless compelling circumstances force us not to".
After more than two decades living in the United States, where he was rumoured to be working for the Central Intelligence Agency, in 2011 he returned home to take part in the uprising against Kadhafi.