The air strikes hit al-Mansoura district, a stronghold for militants and an area which has witnessed several attacks against local security officials since the Saudi-led coalition retook Aden last July from the Iran-allied Houthi militia.
The sources said at least 20 civilians and militants were wounded as well as three members of the security forces.
The strikes targeted the militants who were sitting atop vehicles and one of the strikes hit a local government building.
Intermittent clashes were still going on, they said.
A security official said the strikes, thought to have been carried out by the Saudi-led coalition, were the "second stage" of freeing al-Mansoura from militants.
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There was no immediate comment from the Saudi-led coalition on the strikes.
They come a day after forces loyal to Yemen's president broke a siege by the Houthis around Taiz, Yemen's third biggest city, about 200km northwest of Aden.
Yemen's embattled government has been forced out of the capital Sanaa by the Houthi rebels and is now based in Aden but struggles to impose its authority even there.
The southern city has gone from being one of the world's busiest ports as a former hub of the British empire to a backwater, and then in recent months, a conflict zone.
A Saudi-led coalition began a military campaign a year ago to prevent the Houthis from taking complete control of Yemen.
