Two other blasts were reported from the near Kabul airport. Gunfire continued after the attack and NATO jets were heard flying overhead.
"The attacker was wearing police uniform. When he detonated his explosives, 20 cadets were killed and 20 more were wounded," said a senior Afghan intelligence official.
The bomber managed to place himself in a queue as police trainees were waiting to be searched before entering the academy, the official added.
Taliban spokesperson Zabihullah Mujahid claimed that his outfit was behind the attack on the police academy.
The suicide bombing comes less than 24 hours after a truck bomb tore through central Kabul, killing 15 civilians and wounding 240 others, in the first major attack in the Afghan capital since the announcement of Taliban leader Mullah Omar's death.
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