The spokesman cautioned that the toll could rise.
No group has yet claimed responsibility for the attack.
"Kabul police forces were there to prevent a possible protest when a suicide bomber approached them and detonated his suicide vest", Mujahid said.
The blast happened close to a group of security personnel who were carrying out an operation against illegal drugs and alcohol dealing, officials said.
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.
LG HU80KA 4K Projector Stands Upright
Considering the LG Full HD projectors top out at 2,000 lumens that's an impressive jump up for this beast of a unit. LG said the new HU80KA projector is at par or excels its competitors while still sporting smaller dimensions.
Nokia 6 (2018) is official and it's a speedy upgrade
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The caller said he had shot his girlfriend and would also shoot his parents if officers approached the home. A man was fatally shot by a police officer in what is believed to be a gaming prank called "swatting".
The UN Security Council also condemned "the heinous and cowardly" terrorist attack and underlined the need to bring "perpetrators, organisers, financiers and sponsors of these reprehensible acts of terrorism to justice".
IS claimed responsibility for the December 28 attack, which Afghan President Ashraf Ghani called a "crime against humanity" committed by terrorists.
The capital has become one of the deadliest places in war-torn Afghanistan for civilians in recent months, as the Taliban step up attacks and Isis seeks to expand its presence in the country.
At least 11 people were killed and 25 others were wounded in the latest violent act to rock the Afghan capital.