The Islamists, including Ansar al-Sharia militants, attacked a base of elite special forces who support renegade general Khalifa Haftar, triggering the fighting, said the commander of a Benghazi air base who has also sided with him.
Officials at two hospitals in the area said at least eight soldiers and two civilians were killed, and 15 people wounded.
Fearing the violence might spread, hospitals called on citizens to donate blood, while the education ministry closed schools, forcing the postponement of scheduled final exams.
The Libyan air force retaliated by launching strikes on the assailants, added the officer.
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The air base and the elite special forces unit in Benghazi have thrown their support behind Haftar who last month launched an offensive against Islamists accused of repeated violence in the city.
The latest bloodshed comes a day after Haftar's forces launched fresh air raids on Islamists in Benghazi, including a meeting of Ansar al-Sharia, said General Saqr al-Jerushi who heads air operations.
Authorities have denounced Haftar as an outlaw, but he has won over units from the regular army and air force and says he aims to crush "terrorism" in Benghazi.
Since the 2011 NATO-backed uprising that ousted veteran dictator Moamer Kadhafi, near-daily attacks blamed on radical Islamists have targeted security forces in Benghazi.