The armed forces led by Marshal Khalifa Haftar announced a "great victory" against Islamist militants in Libya's second city of Benghazi on Thursday.

"We now have total control of the Qawarsha sector," 10 kilometres (six miles) west of the centre of Benghazi, said Ahmad Mesmari, spokesman for Haftar's forces.

Mesmari hailed what he termed a "great victory" in what had been a stronghold of Ansar al-Sharia, a group close to Al-Qaeda that is classified as a terrorist group by the United Nations and United States.

Haftar's forces, called the Libyan National Army, were persuing the Islamist militants in Qanfouda, further west, one of the last remaining sectors held by Islamist militants  of the Mediterranean city.

He did not give a casualty toll for the fighting but a military source said Wednesday that 12 of Haftar's soldiers had been killed in clashes since Tuesday.

Thirteen "extremists" died in three days of battle, according to another spokesman for Haftar's forces, Ali al-Thabet, but there was no independent confirmation of that toll.

The US envoy to Libya, Jonathan Winer, on Thursday issued a rare show of support for the forces of Haftar, a controversial and divisive figure in Libya.

"Tough sacrifices by #Libya National Army soldiers this week reported - 20 killed & 40 injured in counter terror fighting in Benghazi," he wrote on Twitter.

Benghazi, birthplace of the 2011 revolution which toppled Libya's longtime dictator Muammar Gaddafi, has been the scene of daily clashes for the past two years between Haftar's forces and Islamist militias holding onto pockets of the city.

Five years after the revolution, the country is embroiled in violence and run by two rival administrations.