The bomber appeared to have meant to attack a crowd gathered to mark the anniversary of the killing of Hazara political leader Abdul Ali Mazari by the Taliban in 1995, but he was stopped before reaching the main gathering.
In December, dozens of people were killed in a suicide attack on a Shi'ite cultural centre claimed by Islamic State, and two months earlier two separate mosque attacks killed at least 72 people.
The Pakistani Taliban has confirmed the death of the son of leader Mullah Fazlullah in a suspected USA drone strike on March 6.
In central Ghazni province, the Taliban attacked a police security post late Thursday, killing four policemen, said Arif Noori, a spokesman for the Ghazni provincial governor.
A spokesman for the Kabul police chief said the bomber was stopped at the checkpoint near the gathering when he detonated explosives.
President Mohammad Ashraf Ghani called the attack a crime against humanity.
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Fazlullah is the leader of Pakistani Taliban and is believed to be hiding in Afghanistan.
The death toll has risen to nine, Waheed Majroh, spokesman for the Health Ministry said.
Members of the local police who were sent to assist the soldiers were ambushed by the Taliban while on their way to the outpost in the remote district of Khwaja Ghar. Mujahid claimed the Taliban had inflicted a far higher number of casualties, but the insurgents often exaggerate their claims.
She said there is a way to end the conflict with the worldwide support and it is now up to the Taliban leaders to respond to the serious offer of talks from the Afghan President. The report could not be independently confirmed because of the area's remoteness.
Information for this article was contributed by Maamoun Youssef and Kathy Gannon of The Associated Press.