The blast came less than a week after an explosion at a school killed 80 people, most of them schoolgirls from the ethnic Hazara Shia Muslim minority.
The force of the explosion flipped the car upside down, killing the city’s District 5 police chief, Mohammadzai Kochi, and his bodyguard.
Meanwhile, the US has said its deal with the Taliban is in the "next phase" as it urged the militants to reduce rising bloodshed.
In recent weeks in Afghanistan, militants have carried out several roadside bombings and rocket attacks in Kabul and other parts. Latest series of explosions appears to be the first coordinated effort for some months.
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