Fighting in recent days has been taking place on the outskirts of Tripoli as LNA forces have been bogged down by groups aligned with the Government of National Accord (GNA).
With more than 560 people wounded since the fighting started on April 4, World Health Organization said it was sending more medical supplies and staff to Tripoli.
On its Twitter feed, the agency denounced "repeated attacks on healthcare workers" and vehicles during the fighting.
"Three medical personnel have been killed and five ambulances have been incapacitated by shrapnel", OCHA said in a Saturday statement.
A bewildering array of militias have sought to take control since his ouster.
During the past week, Eastern-based Libyan forces led by Haftar have been advancing in a push to seize the capital, Tripoli, but troops loyal to Prime Minister Fayez Al-Serraj's internationally recognized government have so far kept them at bay.
The United Nations Support Mission in Libya (UNSMIL) on Sunday condemned attacks on civilian areas and institutions in the Libyan capital Tripoli, which is witnessing violent battles between the UN-backed government forces and the eastern-based army.
Zach Johnson knocks ball off tee with practice swing at the Masters
Because Johnson didn't have the intention of hitting the ball, he was allowed to re-tee and hit again. For those of you who aren't necessarily golf fans, that wasn't supposed to happen.
Al Jazeera's Mahmoud Abdelwahed, reporting from Tripoli, said LNA sources confirmed one of the forces' fighter jets was shot down but added the pilot had "escaped" after using a parachute to eject from the unit.
Libya's Khalifa Haftar was in Egypt on Sunday on a previously unannounced visit, taking time out from his Libyan National Army's march on the Libyan capital to hold talks with his Egyptian sponsor, President Abdel Fattah El Sisi.
Gen Haftar also has the support of some Gulf Arab states and Russian Federation.
With gunfire now echoing through city blocks and tanks rumbling through towns and districts south of Tripoli, many panicked residents have fled their homes.
The sides in the civil war "which were fighting Daesh are now fighting each other", said Tarek Megerisi, a policy fellow with the North Africa and Middle East program at the European Council on Foreign Relations.
The LNA accused the Tripoli forces of an air raid against civilians in the Gasr Ben Ghachir region south of Tripoli.
GNA spokesman Mohamed Gnounou said his forces had carried out 21 air strikes targeting LNA positions and supply lines between Friday and Saturday. But analysts believe the campaign on the capital of a UN-backed government could potentially reignite large-sale fighting among the country's rival powers and undermine global efforts to reunite the fractured North African nation.