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.
"President Sisi stressed Egypt's support for the efforts of counter-terrorism and fighting the extremist groups and militants to achieve security and stability in Libya", Egyptian presidential spokesman Bassam Rady said in the statement.
Observers fear a civil conflict matching the 2011 rebellion that led to the ouster and death of dictator Moammar Gadhafi.
Haftar will ignore calls for peace and continue his bloody offensive on Libya's capital.
Images released by the palace showed a seated Mr Sisi flanked by Gen Haftar and the head of Egypt's intelligence Abbas Kamel in the reception hall of the presidential palace in the Cairo suburb of Heliopolis. Sisi, a former army chief, has led a far-reaching crackdown on Islamists with Egypt and has blamed Libya-based militants for some cross-border attacks. "No matter how obstinate one becomes, there is no solution except a political one", Ghassan Salame said in a Twitter post.
As well as thwarting the United Nations plan, the flare-up threatens to disrupt oil supplies, boost migration to Europe, let Islamist militants exploit the chaos, and worsen Libyans' suffering. The intense fights near the capital have so far killed 121 people and wounded 561, the World Health Organization said.
The fighting killed and injured hundreds of people, and forced thousands of civilians to flee their homes.
But Fayez al-Serraj's National Accord government has managed to halt the advance for now, aided by forces with machine-guns on pickups and steel containers across the road into Tripoli.
A military aircraft belonging to Haftar's forces crashed on Sunday south of Tripoli, the Sky News Arabia news agency reported.
No other details about the meeting were immediately available.
Pro-government forces said they were "searching for the pilot", he added.
His lightning drive appears to have united diverse factions in western Libya in the defense of Tripoli.
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