The group issued a statement claiming that the attack was carried out by one of the suicide bombers of ISIS Khurasan Talha Khurasani.
The statement further added that the attack has inflicted casualties on at least 55 people.
However, the officials said late on Sunday that the attack has left at least 7 dead and while 24 others sustained injuries.
The Kabul police spokesman Hashmat Stanikzai said the attack was carried out at around 3pm local time by a suicide bomber riding a motorcycle.
The convoy was targeted in the vicinity of the 4th police district of the city in Taimani area as they were marching to mark the death of the former Mujahideen leader Ahmad Shah Massoud.
The Ministry of Interior in a statement confirmed that the suicide attack left at least 7 people dead and at least 24 others sustained injuries in the attack.
Another security source had earlier said at least 9 people have been killed and nearly 20 others have sustained injuries.