The bomber struck on Saturday in Jaar, one of a string of towns in Abyan province that were retaken by government troops in June after being held by al Qaeda loyalists for more than a year.
“An al Qaeda suicide bomber detonated his explosives belt during a mourning ceremony organised by the Popular Resistance Committees,” a local militia that fought alongside the army in its month-long counter-offensive, said provincial governor Jamal al-Aqal.
An official at the Razi hospital in Jaar said it had received the bodies of 24 of the dead, while medics said 12 people died of their wounds in three hospitals in the main southern city Aden.
Relatives took the bodies of six of the dead directly from the scene of the attack for burial, local official Mohsen bin Jamila told AFP.
The 37 wounded were being treated in hospitals in Jaar and Aden.
“The victims’ bodies were flying in all directions because the explosion was so powerful,” a witness said.
The deputy head of the municipal authority in Jaar held the government partially responsible for the attack because of its slowness in deploying police to the town after its recapture by the army.
“There is no presence of police in Jaar and other towns of Abyan, while al Qaeda militants remain underground,” said Nasser Abdullah Mansari.
On Wednesday, an attack by al Qaeda militants on a police station in Jaar killed four soldiers and a civilian. Residents have expressed fears that the jihadists could retake the town.
The suspected US drone strike came near the village of Al-Qotn in Hadramawt province in the east of Yemen, another region where al Qaeda has been active.
“A drone fired two missiles at an all-terrain vehicle… killing its five occupants, all members of al Qaeda,” a local official said, requesting anonymity.
Security forces sealed off the scene of the strike, witnesses said.
The United States is the only country that has drones in the region and in recent months has stepped up its strikes on al Qaeda targets in the south and east of Yemen.
Washington regards the Yemen-based al Qaeda in the Arabian Peninsula as the most effective branch of the global jihadist network.
Al Qaeda loyalists have carried out a spate of deadly attacks against the Yemeni security forces and their militia allies since President Abdrabuh Mansur Hadi came to power earlier this year pledging to crush the militants.
Al Qaeda had taken advantage of a nearly year-long uprising against Hadi’s predecessor, veteran strongman Ali Abdullah Saleh, to seize large swathes of the south and east.
In July, Yemen announced it had placed its security services on high alert to prevent “terrorist” attacks after it uncovered a plot to launch assaults against security and military checkpoints.