The attacker struck near the old interior ministry building, interior ministry deputy spokesman Nasrat Rahimi told AFP.
"The suicide bomber used an ambulance to pass through the checkpoints. He passed through the first checkpoint saying he was taking a patient to Jamuriate hospital and at the second checkpoint he was recognised and blew his explosive-laden car," interior ministry deputy spokesman Nasrat Rahimi told AFP.
The Taliban claimed responsibility for the attack outside the European Union delegation and interior ministry offices.
An AFP reporter said he saw "lots of dead and wounded" people in a nearby hospital. A popular stationery market was near the site of the blast, the force of which shattered windows of surrounding buildings and caused some low-rise structures to collapse.
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In chaotic scenes at the Jamuriate hospital, which is the nearest medical facility to the blast, overwhelmed doctors and nurses rushed to treat dozens of wounded lying in the corridors.
AFP reporters heard a loud explosion that shook the windows of their compound a few kilometres away, and photos shared on social media purportedly of the blast showed a huge plume of smoke rising into the sky.
The explosion happened in a busy part of the city where the High Peace Council has offices. Kabul police headquarters is also in the vicinity of the blast.
"It targeted our checkpoint. It was really huge -- all our windows are broken," said Hassina Safi, a member of High Peace Council, which is charged with negotiating with the Taliban.
The explosion comes exactly a week after Taliban militants stormed a luxury hotel in Kabul, killing at least 22 people, the majority foreigners.
A security alert issued to foreigners on Saturday morning warned that the Islamic State group, which has terrorised the city in recent months, was planning "to conduct aggressive attacks" on supermarkets, shops and hotels frequented by foreigners.
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