Sixteen people, including six soldiers, six militants and four bystanders, were killed in the twin car bombing, the interior ministry said.
The US embassy says none of its staff has been hurt.
Witnesses said gunmen raked the Yemeni police detachment outside the heavily fortified embassy compound before a suicide bomber blew up a car right by the entrance, setting off a fire.
They spoke of a series of explosions as the embassy came under rocket as well as small arms fire, in what is the second attack on the US mission this year.
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