The bombing came hours after gunmen shot dead an army officer as he came out of a grocery shop in Aden, capital of southern Yemen, which has seen a spike in attacks on security forces.
In today's attack, the car exploded at the entrance of the post in a residential neighbourhood of Mukalla, the provincial capital of Hadramawt, causing damage to it and other buildings, said a security official.
Guards had opened fire on the car driven by an "Al-Qaeda suicide bomber" as it approached the entrance, the official said, speaking on condition of anonymity.
Yesterday, senior AQAP member Qassem al-Rimi threatened in an online video to strike back at any party involved in the drone campaign that has killed dozens of suspected jihadists.
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The Yemeni army launched an offensive on Tuesday against hideouts of the Al-Qaeda affiliate, mainly in the south where the militants are strongly rooted.
Late yesterday, gunmen shot dead Colonel Sanad al-Mayshari in the Mansura neighbourhood of Aden, police officials said.