Zabihullah Mujahid said the attack, which hit a demonstration by thousands of members of the mainly Shia Hazara ethnic minority, was carried out by enemy circles.
The Taliban denied responsibility for a suicide attack on a demonstration in Kabul that killed at least 29 people and wounded 142 on Saturday.
Taliban chief spokesman Zabihullah Mujahid said in a statement that the movement "did not have any involvement or hand in this tragic attack."
He said the attack, which hit a demonstration by thousands of members of the mainly Shia Hazara ethnic minority, was carried out by "enemy circles".
Meanwhile, the Islamic State claimed responsibility on Saturday for a suicide attack in Kabul targeting members of the country's Shi'ite Muslim minority, the group's Amaq news agency reported.
"Two fighters from Islamic State detonated explosive belts at a gathering of Shi'ites in... the city of Kabul in Afghanistan," Amaq said in a brief news alert.
Suicide bombers killed at least 61 people and wounded over 200 in an attack on a large demonstration by Afghanistan's Hazara minority, a mainly Shia group estimated to comprise about 9 percent of the population.
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