A military aircraft belonging to Haftar’s forces crashed on Sunday south of Tripoli, the Sky News Arabia news agency reported.
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.
According to the Sky, the jet pilot managed to eject from the aircraft before the crash, but it is unclear whether he is alive.
The development comes shortly after Haftar met with Egyptian President Al-Sisi, with the former promising to support counterterrorism efforts in Libya.
"The president (Sisi) affirmed Egypt's support in efforts to fight terrorism and extremist militias to achieve security and stability for Libyan citizens throughout the country", according to a statement by the Egyptian president’s office.
The Egyptian president has been a supporter of the LNA, which holds parts of Libyan territories in the country’s east and started an offensive on April 4 to claim Tripoli.
Haftar’s forces have been locked in a military standoff with the GNA for 10 days, accusing the rivals of allying with terror groups and vowing to drive the latter from the country. The intense fights near the capital have so far killed 121 people and wounded 561, the World Health Organization said.
The spike in the violence of recent weeks has marked an escalation of the long-standing conflict in Libya, which has been ongoing since 2011, when protests led to the ouster of then-leader Muammar Gaddafi. The country has been split between warring parties, with the LNA-backed parliament sitting in Tobruk in the east, and the GNA controlling the west of the country.