In the central city of Taez, meanwhile, pro-government forces launched a manhunt for 1,200 escaped prisoners.
Both Aden and Taez have seen heavy fighting as loyalists of exiled President Abedrabbo Mansour Hadi battle to repel Shiite Huthi rebels with the support of a Saudi-led air war launched in March.
Aden was Hadi's last refuge before he fled into exile in neighbouring Saudi Arabia in March and his supporters have been battling to defend it against the rebels and renegade troops.
The rocket fire began before dawn when the streets were busy ahead of the daytime fast observed by Muslims during the holy month of Ramadan.
A fresh salvo of rockets later in the morning hit mourners burying some of the dead from the earlier fire, the spokesman and witnesses said.
The city's health chief Al-Khader Laswar said at least 31 people were killed, including three women and two children, while more than 100 others were wounded.
Civilians were seen carrying bloodied bodies and calling for help as they piled them into vehicles and drove them to hospitals.
A coalition strike in neighbouring Lahj province killed 13 rebels, an official said.
Yesterday, Human Rights Watch said strikes on the rebel stronghold of Saada in Yemen's northern mountains had destroyed houses, markets and a school, in what could amount to war crimes.
Across the border in the Saudi city of Jeddah, Yemen's exiled Prime Minister Khaled Bahah accused the rebels of committing a "war crime" in Aden by attacking residential areas, laying siege on the city, and forcing aid vessels to turn back.
UN aid chief Stephen O'Brien met with heads of agencies to discuss the crisis in the impoverished Arabian peninsula country.
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