Seventeen civilians were among those killed in Aden since yesterday, as well as 10 fighters loyal to President Abedrabbo Mansour Hadi, a medic said.
At least 26 rebels were killed, according to an army source, who said dozens more people were wounded in the fighting across several Aden neighbourhoods.
Witnesses said that clashes continued today as rebels tried to seize the city's port.
Yemeni President Abedrabbo Mansour Hadi took refuge in Aden in February after the Shiite Huthi rebels seized power in the capital Sanaa, but left for Saudi Arabia last month as they advanced on the city.