At least 20 rebels were killed, and two tanks and four armoured vehicles destroyed, in the overnight air strikes on a convoy headed out of Yemen's largest air base, Al-Anad, provincial official Abedrabbo al-Mihwali said.
The base was the main watching post for a long-running US-led war on Al-Qaeda in Yemen, and its evacuation by Western troops as the rebels advanced last month has created a vacuum that the jihadists have exploited to make big territorial gains.
Most of the rebels were killed in ambushes on the Dar Saad quarter of the southern city, Yemen's second largest.
In Taez, in the central highlands north of Aden, at least 16 people were killed as soldiers who have remained loyal to exiled President Abedrabbo Mansour Hadi put up fierce resistance to an attack on their base by Huthi Shiite rebels and renegade troops.
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Three civilians were among the dead when a stray shell hit their home, a military source and residents said.
The support of army units still loyal to longtime strongman Ali Abdullah Saleh, ousted in 2012 after a bloody year-long uprising, has been crucial to the insurgents' progress.