The Taliban, the largest Islamist militant group in Afghanistan, said in a statement they were not involved in the attack. A top Afghan political leader, Abdullah Abdullah, was present at the event but escaped unharmed.

Fifty-five people were wounded, according to the Afghan ministry of health.

"The attack started with a boom, apparently a rocket landed in the area, Abdullah and some other politicians ... escaped the attack unhurt," Abdullah's spokesman, Fraidoon Kwazoon, who was also present, told Reuters by telephone.

Broadcaster Tolo News showed live footage of people running for cover as gunfire was heard.

A health ministry spokesman said the casualty toll could rise. Dead and wounded were being ferried from the site by ambulance.

A NATO source said that the death toll was slightly higher: more than 30 killed, with 42 wounded, 20 of whom were in a serious condition.

A ministry of interior spokesman said that operatations were continuing to secure the area around the attack.

The gathering marked the anniversary of the death of Abdul Ali Mazari, an ethnic Hazara leader who was killed in 1995 after being taken prisoner by the Taliban. Several people were killed in a similar attack on the same commemoration last year, which Islamic State said was carried out by its militants.

President Ashraf Ghani tweeted that the attack was "a crime against humanity and against the national unity of Afghanistan".

Abdullah, who escaped, was runner-up in the last three Afghan presidential elections, each of which he disputed. He has served as chief executive of a coalition government since 2014 and is also a former foreign minister.

Ghani said he had telephoned Abdullah, his longtime political rival. Abdullah is contesting an Electoral Commission announcement last month declaring Ghani the winner of September's presidential election.

Hazaras are mostly Shi'ite Muslims. Minority Shi'ites have been repeatedly attacked by Sunni Muslim militant groups in Afghanistan.

The United States has been trying to spearhead efforts towards a lasting peace arrangement. Violence decreased during a seven-day hold-down agreement with the Taliban leading up to last Saturday's deal, though the Taliban has since resumed attacks on Afghan forces.

A senior Western security official said all checkpoints in Kabul were on high alert.

"It's too early to say but for now we are intensifying security," the official said.