The militants launched an assault on the AU force's heavily fortified headquarters in Mogadishu yesterday, killing three soldiers from the union's local peacekeeping mission known as AMISOM and a civilian contractor.
"The security forces foiled the attack and killed four of the attackers, and we have arrested four suspects," Somali interior ministry spokesman Mohamed Yusuf said. "Four other people, among them (an) airport worker, were also killed."
Shebab claimed its militants had managed to keep fighting into today, although officials said the attack was brought to an end late yesterday.
The Shebab, who are fighting to topple Somalia's internationally-backed government, said it carried out the attack against what it said were "Ugandan mercenaries".
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The AU force headquarters is a fortified structure located on the grounds of the Mogadishu airport, which is also under high security.
The AMISOM force, deployed since 2007, currently counts some 22,000 African Union troops.
They have managed to push Shebab militants out of the capital, but the Islamists still hold large swathes of territory in the south and centre of the country.