Reports said not less than 20 rebel fighters were killed on Wednesday in the fight to control the city's Masheeq neighbourhood, an area where a palace belonging to exiled President Abd-Rabbu Mansour Hadi is located.
Masheeq was believed to be the last remaining stronghold in Aden for the Houthi rebels, who have been pushed out of Yemen's second largest city over the past two weeks.
Fighters for the Popular Resistance - an anti-Houthi southern militia - have largely been responsible for the push.
Sources told Bloom Gist that the offensive came as Aden's international airport reopened on Wednesday, with a Saudi Arabian plane landing with military supplies.
Exiled Vice President Khaled Bahah last Friday said on his Facebook account that Aden had been liberated and that the government will try "to restore life" to the city.
However, the Houthis have consistently rebuffed claims that they have lost control of the city, which they captured in March.
Several ministers and top intelligence officials of the exiled Yemeni government returned to Aden last week, including the ministers of the interior and transport, a former interior minister, the intelligence chief and the deputy head of the house of representatives.
