Egypt's presidential palace has not released details on Haftar's talks with President Sisi.
Egypt has supported Haftar's drive against Islamic militants in the east and south of its western neighbour, providing both funding and arms to his LNA.
The 75-year-old Haftar's push for Tripoli took many by surprise and has brought calls from round the world for a ceasefire. Egypt has said that it did not think a military solution to Libya's divisions was viable.
In March 2016, GNA chief Fayez al-Sarraj arrived in Tripoli to set up a new government, but the Haftar-allied administration in the eastern city of Tobruk refused to recognise its authority. 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. It did not specify whether they were fighters or civilians.
His move is the latest in a cycle of conflict and anarchy since the 2011 toppling of former dictator Muammar Gaddafi.
Troops loyal to Libya's internationally recognised government have shot down a fighter jet belonging to the eastern forces under the command of Khalifa Haftar, on the same day the renegade general held talks with Egypt's president in Cairo. Moreover, militias, mostly Islamist, have held sway over large regions, particularly in the west and south of the country.
Three dead in horrific plane crash into helicopter near Mount Everest
The airport, built in 1964, is rated as one of the most risky airports in the world due to strong tailwinds and a short runway. Seven people, including the country's tourism minister, were killed in February when a helicopter crashed in the hilly east.
Military sources within the United Nations-backed Government of National Accord (GNA) said the jet operated by the self-styled Libyan National Army (LNA) was downed on Sunday in Tripoli's southern outskirts, as fighting for control of the capital rages.
"Three medical personnel have been killed and five ambulances have been incapacitated by shrapnel", OCHA said in a Saturday statement.
WHO's Libya Twitter account posted an update of "casualties" and said it was "sending medical supplies, health staff support for first- and second-line responders".
In another, earlier tweet, it denounced "repeated attacks on health care workers, vehicles" during the fighting, which began on April 5.
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.
United Nations envoy Ghassan Salame said a school was bombed in the town of Ain Zara, around 15 kilometres southeast of Tripoli, without saying who was responsible. Both sides have carried out airstrikes on the town, and a spokesman for the Libya National Army said it has stepped up strikes on its rivals in the past two days.
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