The number of casualties has been confirmed by Ministry of Public Health and Kabul Police, reported TOLO News.
"The bomber came from among the protesters and targeted our police forces", Rahimi said, adding the attacker was wearing civilian clothes.
There has been an increase in security since last May when a truck bomb in the diplomatic quarter killed 150 people and wounded around 400 others.
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Kabul has suffered repeated suicide attacks in recent weeks.
In a statement Thursday, President Ashraf Ghani called the attack "inhumane" and against the tenets of Islam. According to available information, a suicide bomber blew himself up near a group of policemen.
The Amaq news agency of the militants said a suicide bomber targeted police and intelligence officers busy in an operation in the Banayee area of the city.
On Wednesday, Afghanistan's spy agency announced it had busted a 13-member IS cell in Kabul that had been hatching "a series of big terrorist attacks" in the city.