They said the bomber detonated a belt of explosives he was wearing amid hundreds of soldiers lining up to collect their salaries in the city's Solban army base.
The officials spoke on condition of anonymity because they were not authorized to brief the media.
Waleed Rashed, a soldier in the base, arrived at the scene shortly after the attack to find the area littered with bodies and blood.
"I could hear the wounded soldiers screaming for help," he said. Private cars were used to ferry the wounded to hospitals before ambulances arrived, he added.
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The terror network's branch in Yemen is thought to be the world's most active. It is known to have a presence in Aden, where a loose coalition of troops loyal to the internationally recognized government of President Abed Rabbo Mansour Hadi, local militias and jihadi groups control the city.
The troops and jihadi groups are fighting Shiite rebels, who in 2014 seized Yemen's capital, Sanaa, and later swept much of northern Yemen. Their advances forced Hadi to flee the country and seek shelter in neighboring Saudi Arabia.
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