Western powers and the Gulf have been divided over a push by Haftar’s forces to seize Tripoli, undermining calls by the United Nations for a ceasefire.
Both sides claimed progress in southern Tripoli on Saturday, but no more details were immediately available.
A Reuters TV cameraman visiting the southern Khalat Furgan suburb heard heavy shelling but saw no apparent change in the frontline.
On Friday, two children were killed in shelling in southern Tripoli, residents said. The fighting has killed 227 people and wounded 1,128, the World Heath organization (WHO) said before the air strikes.
On Thursday, both the United States and Russia said they could not support a U.N. Security Council resolution calling for a ceasefire in Libya at this time.
Russia objects to the British-drafted resolution blaming Haftar for the latest flare-up in violence when his LNA advanced to the outskirts of Tripoli earlier this month, diplomats said.
The United States did not give a reason for its decision not to support the draft resolution, which would also call on countries with influence over the warring parties to ensure compliance and for unconditional humanitarian aid access in Libya.