But three loyalists of former general and longtime US exile Khalifa Haftar were killed in the attack on a villa outside the eastern city, the commander told AFP.
"A suicide bomber in a vehicle packed with explosives attacked a villa where we had gathered," said General Sagr al-Jerushi, who heads the air wing Haftar has deployed in his attacks.
"Three of our soldiers were killed," Jerushi said, adding that he himself had been "lightly wounded" in the attack.
The former general claims his forces represent the legitimate Libyan army and has won the support of regular army units in the city including the special forces.
But even though he denies any political ambitions, the outgoing Islamist-led parliament in Tripoli accuses him of plotting a coup and has branded him an outlaw.
Since the 2011 uprising that toppled and killed longtime dictator Muammer Gaddafi, the country has been awash with weapons.
Militias of former rebels who fought to oust the Gaddafi regime have refused to hand over their weapons and control swathes of territory across the country.
Al-Qaeda in the Islamic Maghreb on Sunday urged Libyans to fight Haftar, labelling him an "enemy of Islam".
Ansar al-Sharia, a radical Islamist group in Benghazi classified by Washington as a "terrorist organisation," has warned that Haftar could suffer the same fate as Gaddafi, who was killed by rebels in October 2011.
Its forces have borne the brunt of the offensive led by Haftar.
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