An air strike hit a hospital in Derna in eastern Libya on Sunday, killing four people including a woman and her child and two anti-government fighters, a doctor said.

"There are four dead -- a nurse, her 10-year-old son and two members of the Shura Council," radiologist Dr Mohamad al-Jeddayimi at Al-Wehda hospital told AFP.

In its own statement, the Mujahedeen Shura Council said the attack was in the area of the Faculty of Medical Technology Science in the Bab Tobruk district of eastern Derna came at 0400 GMT.

The Mujahedeen Shura Council of Derna is a coalition of Islamist militias in the city.

It was formed to oppose forces of the controversial General Khalifa Haftar, head of forces loyal to the internationally recognised authorities based in the east.

Jeddayimi said the nurse and her son were killed in a direct hit on Al-Wehda hospital's urology department, adding that the unit was "completely destroyed".

The hospital is near the medical faculty in Bab Tobruk.

No claim of responsibility has been made, and forces loyal to the recognised government did not report any air strike in the area on Sunday.

The coastal city of Derna is 1,100 kilometres (680 miles) east of the capital Tripoli.

The Mujahedeen Shura Council of Derna that controls it is a motley mix of Islamist militias that include Ansar al-Sharia, which is close to Al-Qaeda.

Derna has also come under regular attack by the Islamic State group which has positions on its outskirts after being ousted from the city itself in July last year.

On January 21, IS again tried to enter Derna but was repulsed by local forces.

The jihadist group moved into Libya in 2014, becoming yet another player in the lawless North African state where rival governments and militias are battling for control of territory and major oil reserves.