Yemeni loyalist forces said they advanced Monday into the last district of the southern port city of Aden still held by Iran-backed rebels, seeking to flush out the remaining insurgents.

Fighters from the pro-government Popular Resistance "have regained control of most of al-Tawahi district," including the presidential residence, said spokesman Ali Ahmehi.

The southern fighters also pushed the Shia Houthi rebels and allied forces loyal to former president Ali Abdullah Saleh out of the region's military headquarters and the naval base, he told AFP.

"A wide combing operation is under way to flush out" rebel holdouts, he said, adding that remaining insurgents had taken positions on several rooftops.

Loyalist forces backed by Saudi-led warplanes have regained control of most of Aden since an assault dubbed "Operation Golden Arrow" began on Tuesday.

Clashes have however continued despite the government's declaration on Friday of the city's "liberation" after four months of ferocious fighting.

Rebel bombardment on Sunday killed 57 civilians in the Dar Saad neighbourhood in the north of the port city, according to local health chief Al-Khader Laswar.

Two ministers from the government in exile in Saudi Arabia returned to Aden this weekend, and on Sunday they toured the devastated city.

A Saudi-led Arab coalition launched an air campaign against the rebels in March after President Abedrabbo Mansour Hadi was forced to flee to Riyadh.

More than 3,200 people have been killed in the fighting -- many of them civilians, the UN says.