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"A suicide bomber got into the supermarket and blew himself up," said the officer on condition of anonymity.
Kabul police spokesman Hashmat Ullah confirmed the explosion.
"The explosion took place at the Finest supermarket in the centre of Kabul near many embassies," he said.
"There are dead," he said without being able to specify the number.
An AFP journalist on the spot saw two dead, and one person severely wounded.