It was not immediately clear if the plane was shot down or suffered a malfunction, added General Sagr al-Jerouchi, chief of air operations for dissident general Khalifa Haftar.
A witness, who said he saw a parachute open before the crash, added that the warplane had just attacked militant positions.
Weekend fighting in Benghazi, cradle of the 2011 revolution that ousted dictator Moamer Kadhafi, killed dozens of people, mostly soldiers.
Combat erupted on Saturday when militants attacked the headquarters of a special forces unit near the city centre.
Since May, clashes have taken place in Benghazi on an almost daily basis.
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The Arab spring is a big joke . The Arabs were better off two decades back .