The current violence pits Haftar's self-styled Libyan National Army, which backs a rival government in the east of the country, against an array of militias that support the Tripoli administration.
The Libyan commander has modelled his political style of authoritarian leadership after El-Sisi, himself an army general turned president.
Egypt has in the past blamed Libyan-based militants for a series of cross-border attacks against its security forces and minority Christians traveling to remote desert monasteries.
The UN-backed GNA later issued a statement saying that it had downed a military jet belonging to the Eastern forces after it attacked the positions of its forces.
The intense fights near the capital have so far killed 121 people and wounded 561, the World Health Organization said.
Haftar has defied global calls to halt his battle against fighters loyal to the UN-backed Government of National Accord based in Tripoli.
Since the ouster and killing of former Libyan leader Muammar Gaddafi in 2011, Libyan factions have been engaged in a civil war that escalated in 2014, resulting in splitting power between two rival governments in the northwestern city of Tripoli and the northeastern city of Tobruk respectively.
WHO's Libya account said on Twitter the organisation was sending medical supplies and more staff to Tripoli, while denouncing "repeated attacks on health care workers, vehicles" during the fighting which began on 4 April.
In addition to ground fighting, both sides conduct daily air raids and accuse each other of targeting civilians.
More than 13,500 people had been displaced by the clashes, while more than 900 residents are living in shelters, according to the UN's office for humanitarian affairs, or OCHA.
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.