Forces loyal to Marshal Khalifa Haftar on Monday retook a district in Libya's Benghazi from Islamist militants after fighting that killed nine soldiers in two days, a military source said.

"We now control the district of Abu Sneib" in the southwest of the city, said a commanding officer in the army headed by Haftar, who backs the parliament in the country's east.

"Our forces now completely surround the Qanfuda area" nearby, the same source said.

The source said 52 troops had died in fighting since January 1 in and around Benghazi.

Haftar has managed to retake a large part of the eastern coastal city from Islamist militants since Benghazi came under their control in 2014.

But Islamist militants still control the central districts of Al-Saberi and Souq al-Hout.

These militant groups include the Revolutionary Shura Council of Benghazi, an alliance of Islamist militias that includes the Al-Qaeda-linked Ansar Al-Sharia.

Benghazi was the cradle of the 2011 uprising that toppled and killed leader Muammar Gaddafi.

Libya has since fallen into chaos, with a UN-backed unity government failing to assert its authority over the country.

The parliament based in the eastern city of Tobruk has refused to recognise the Tripoli-based Government of National Accord.