The bomber, who was on foot, detonated his explosives vest as he walked by the vehicle in the western part of the city, said Najib Danish, the Interior Ministry's deputy spokesman,
The casualties include both court workers and civilians and the explosion also wounded four people.
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The vehicle belonged to the judiciary department in neighbouring Maidan Wardak province and was taking the workers there when it came under attack.
Within claimed responsibility for the bombing. The claim came from Zabihullah Mujahid, a Taliban spokesman, in an email sent to the media.
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The attack came as the Taliban named a new leader following Mullah Akhtar Mansour's death in a U.S. drone strike on Saturday.
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The last major attack in Kabul was on April 19, when a massive bomb killed 64 people and wounded hundreds. The Taliban also claimed that bombing.
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