According to a short statement posted by the pro-ISIS website, Amaq Agency, the attack was carried out by two suicide bombers of the terror group.
The statement further added that the two ISIS militants detonated their explosie belts amid a Shiite gathering in the Deh Mazang area in Kabul.
This comes as the Taliban group earlier rejeccted hand in the deadly attack and called it an act aimed at sparking divisions among the communities in the country.
Taliban group spokesman Zabiullah Mujahid said the group condemns any move that lead to creation of divisions, including ethnic and religious divisions among the people of Afghanistan.
Without elaborating further Mujahid said the attack was carried out by the enemies.
The Ministry of Public Health (MoPH) officials said at least 61 people have been killed and over 200 others sustained injuries in the attack.
The incident took place as hundreds of thousands of people gathered in the area to protest against the implementation of TUTAP project via Salang pass.