So-called Islamic State has said it was behind an attack on a protest march in the Afghan capital, Kabul, that killed 80 people and wounded 230.

The IS-linked Amaq news agency said two fighters "detonated explosive belts at a gathering of Shia" in Kabul.

The attack in Deh Mazang square targeted thousands from the Shia Hazara minority who were protesting over a new power line, saying its route bypasses provinces where many of them live.

The Taliban have condemned the attack.

Spokesperson Zabiullah Mujaheed sent an e-mail to the media saying they were not behind it.

Self-styled IS has a presence in eastern Afghanistan but has not previously admitted carrying out assaults in the capital.

An Afghan intelligence source told the BBC that an IS commander named Abo Ali had sent three jihadists from the Achen district of Nangarhar province to carry out the Kabul attack.

Demonstrators from Afghanistan's Hazara minority attend a protest in Kabul, Afghanistan July 23, 2016. Photo: Reuters

The interior ministry said only one attacker had successfully detonated an explosives belt. The belt of the second failed to explode and the third attacker was killed by security forces.

'Death to discrimination'

Afghan President Ashraf Ghani addressed the nation on TV, declaring Sunday a day of national mourning.

"I promise you I will take revenge against the culprits," he said.

He had earlier issued a statement saying: "Peaceful protest is the right of every citizen, but opportunist terrorists infiltrated the crowds and carried out the attack."

A freelance journalist working for BBC Afghan said blood and body parts were everywhere, with debris strewn around.

A large part of Kabul's city centre had been sealed off for the protest march.

The demonstrators had waved banners and chanted "death to discrimination", angry that the 500kV power transmission line from Turkmenistan to Kabul would not pass through Bamyan and Wardak provinces, which have large Hazara populations.

The Hazaras - mostly Shia Muslims - live mainly in the centre of the country.

They complain of persistent discrimination, especially during Taliban rule in the late 1990s, when many of them fled to Pakistan, Iran and Tajikistan.