The Shiite Houthi forces and their allies withdrew from Crater neighborhood as well as one of Aden's presidential residences which they seized a day earlier, residents and a local official were quoted by Reuters as saying.
Their withdrawal followed overnight clashes and an air strike on the presidential palace at Ma'ashiq, overlooking Crater. At least one Houthi tank was destroyed and another taken over by President Abd-Rabbu Mansour Hadi's loyalists, they said.
The Houthis, fighting alongside soldiers loyal to former president Ali Abdullah Saleh, emerged as the strongest force in Yemen after they took over the capital Sana'a in September.
Last month they advanced on Aden, where Hadi had retreated, prompting the response from Riyadh. Nine days of Saudi-led air strikes have destroyed much of their equipment and cut off any chance of outside reinforcement, but failed to halt their march on the port city.
Aden residents said the streets of Crater neighborhood, deserted on Thursday after the Houthis swept in, were busy again on Friday after the attackers pulled back to the adjacent district of Khor Maksar.
Early on Friday warplanes from the coalition dropped crates of weapons and medical supplies by parachute over Tawahi, a district on the far end of the Aden peninsula which is still held by Hadi loyalists, fighters told Reuters.