"A MiG-21 was shot down by a heat-seeking missile," said Mohammad Ghunem, spokesman for the forces of strongman Khalifa Haftar, who is battling to oust jihadists from Libya's second city.
"The plane, targeted by terrorist groups, crashed in the district of Suq al-Hut but its pilot survived."
He said the jet was hit as it carried out a raid on the last bastion of "extremists" in the city's Mediterranean seafront district of Al-Saberi.
The pilot, Adel Abdullah Bushisha, was able to eject and landed by parachute in the east of the city, he said.
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Benghazi, which fell to Islamist groups in 2014, has been the scene of deadly fighting between them and forces loyal to Haftar, who controls much of eastern Libya in defiance of the UN-backed unity government in Tripoli.
Haftar's self-declared Libyan National Army (LNA) has managed to retake a large part of Benghazi, the birthplace of the 2011 revolution.
But the LNA says jihadists are still present in the central districts of Al-Saberi and Suq al-Hut.