A drone strike earlier this week against an Al-Shabab vehicle carrying explosives prevented an "imminent threat to the people of Mogadishu", the U.S. African Command said.
The attacker disguised himself in a police uniform to access the camp, Afrah said.
Witnesses said the police were gathering for their early morning parade, and were crowded in an open square when the bomber attacked.
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Soon after the attack, Islamist militant group, al Shabaad claimed responsibility for the attacks.
However, the Al-Qaeda-affiliated Shabaab has repeatedly attacked police officers in its decade-old battle to overthrow successive internationally-backed governments in Mogadishu. The insurgents said they killed 27 police officers.
Police spokesman Maj Mohamed Hussein said officers had been rehearsing for national Police Day celebrations later this month.
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The U.S. military has carried out at least 30 airstrikes this year against the Somalia-based extremist group al-Shabab and a small but growing presence of fighters linked to the Islamic State group.
In October, a huge truck bombing blamed on the Shabaab killed as many as 512 people, levelling buildings in the capital's busy Kilometre 5 neighbourhood.
A 22,000-strong African Union force (Amisom) is in Somalia trying to help the government recapture territory from militants.
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