Terror outfit Isis has claimed responsibility for the twin suicide blasts that shook a peaceful rally in Kabul, reportedly killing at least 61 people and injured many more.

The Taliban denied any involvement in the incident, and even condemned the attack.

"Did not have any involvement or hand in this tragic attack," Zabihullah Mujahid, the Taliban chief spokesman, was quoted as saying in a statement by Reuters.

"Two Daesh fighters detonated their explosive belts amid a Shiite gathering in the Dehmazang area in Kabul, Afghanistan," Isis mouth piece Amaq news agency said. Afghan security officials have also verified the claim.

The attack was organised by a Daesh member by the name of Abu Ali who is a resident of Achin district in Nangarhar in Afghanistan, according to an anonymous senior security official quoted by TOLO News.

Afghan President Ashraf Ghani's spokesperson claimed that central government had issued a warning to the organisers of the protest as they had anticipated a possible terrorist attack. "Peaceful protest is the right of every citizen, but opportunist terrorists infiltrated the crowds and carried out the attack, killing and injuring a number of citizens including some security forces," he said. 

Ghani denounced and condemned the 'act of terrorism' minutes after the deadly bombings took place but social media users were quick to attack the Facebook post written by Ghani's deputy spokesman. "Why don't you (government) act instead of offer verbal sympathy," one user said.

Protesters belonging to the minority Hazara community had gathered in a peaceful demonstration at Kabul's Dehmazang Circle to oppose the government's decision of denying their region essential infrastructure through their plans of rerouting a power line.

Officials confirmed that three suicide bombers were present at the rally, the first one detonated self, the second's vest was defective and the third bomber was killed by NDS officers.

An eyewitness told TOLO News that the person who detonated self was dressed in a burqa and stood among demonstrators of the minority community.

The dead and wounded had been taken to nearby hospitals, said Mohammad Ismail Kawousi, a spokesman for the ministry of public health, even though reports said that ambulances had a tough time reaching the site as authorities had preemptively blocked key intersections with stacked shipping containers to impede movement of the protesters.