Sisi has been an ardent supporter of Haftar's self-styled Libyan National Accord (LNA), which control swathes of eastern Libya and launched an offensive on 4 April to take the capital where the internationally recognised Government of National Accord (GNA) is based.
"We have lost one of our MiG-21 fighters [NATO reporting name: Fishbed] after the pilot lost control of the aircraft". No further details were available.
The United Nations' office for humanitarian affairs said more than 13,500 people had been displaced by the clashes, while more than 900 residents are living in shelters.
As well as fighting on the ground, the two sides have launched daily air raids and accuse each other of targeting civilians.
While some pro-Haftar media had predicted a quick victory, Tripoli government forces have halted him about 11 km (7 miles) from the center near an airport that was largely destroyed in a previous bout of fighting five years ago.
The situation remained "very tense" on Tripoli's southern outskirts, Abdelwahed said, with the mass displacement constituting a "crisis" for authorities attempting to rehouse those forced to flee.
The meeting was scheduled to bring Haftar and al-Serraj together in the southwestern town of Ghadames on April 14-16.
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.
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.
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.
On Saturday, the Tripoli-based Interior Minister of the Presidential Council's government Fathi Bashagha accused the United Arab Emirates (UAE) of reportedly sending Haftar military support in "clear violation of the global law". "No matter how obstinate one becomes, there is no solution except a political one", Ghassan Salame said in a Twitter post.