Fighters from the pro-government Popular Resistance "have regained control of most of Al-Tawahi district," including the presidential residence, said spokesman Ali al-Ahmadi.
The southern fighters also pushed the Shiite Huthi 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.
Ahmadi said 40 other rebels have been taken prisoner, but Al-Maashiq presidential palace in the downtown district of Crater remains in rebel hands.
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Loyalist forces backed by Saudi-led warplanes have regained control of most of Aden since an assault dubbed "Operation Golden Arrow" began last Tuesday.
Clashes have rumbled on, however, 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.
Transport Minister Badr Basalmeh told journalists in the city that a technical team had arrived from the United Arab Emirates to repair the control tower and passenger terminal at Aden international airport, which was heavily damaged in clashes before rebel forces were driven out.
Elsewhere in southern Yemen, Saudi-led coalition warplanes today carried out several raids on rebel positions, especially Al-Anad air base in Lahj and the neighbouring province of Dhaleh, military sources said.