Twenty members of a single family were wounded when a rocket slammed into their home near an army base in Libya's second city Benghazi overnight, medical and security sources said Friday.

The family's home lies close to the headquarters of the army's special forces unit in Benghazi, which is backing a rogue general who has vowed to crush Islamists in the city, a security official said.

Another rocket hit the base but caused no casualties, the official said.

The 20 family members all suffered shrapnel wounds when the rocket hit their home in the central Abuhdima neighbourhood, Al-Huari hospital spokesman Hani al-Aribi said.

Rogue general Khalifa Haftar launched an assault on Islamists in the city last Friday in which at least 79 people were killed.

That prompted the government to brand him an outlaw and claim he was attempting a coup, but Haftar says he is on a mission to rid Libya of "terrorists" and insists he has no interest in power.

Islamists have been blamed for almost daily attacks in Benghazi since the 2011 uprising that toppled and killed long-time dictator Muammar Gaddafi.

They have targeted foreigners and judges as well as security force personnel.

The special forces, who have suffered heavy losses in the attacks, threw their support behind Haftar earlier this week.