War planes struck Huthi positions in the north of the port city, killing six fighters, after fighting killed seven rebels and eight soldiers loyal to exiled President Abedrabbo Mansour Hadi, the sources said.
The clashes followed Huthi advances in west Aden, backed by renegade troops, that saw the rebels take control of a military base late yesterday.
Fighting continued today around the base, according to military sources.
Rebel shelling of several residential neighbourhoods overnight killed at least five people, including a child, city health chief Al-Khader Laswar told AFP.
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A Saudi-led coalition launched air strikes against rebels in Yemen in March, after the Huthis seized control of much of the country and encroached on Aden, where Hadi had taken refuge before fleeing to Riyadh.
Peace talks last month in Geneva between representatives of the exiled government and the Huthis failed to settle the deadlock.
More than 2,600 people have been killed in the impoverished Arabian Peninsula country since March, according to UN figures.