A resurgent Taliban has been blamed for much of the increased violence in Afghanistan since United States and North Atlantic Treaty Organisation forces concluded combat missions in 2014.
Local Hazara leader Mohammad Mohaqiq told the Kabul gathering that the explosion was an attempt to terrorize Afghans.
The most lethal suicide bombing against Hazaras came in 2016, killing more than 80 people.
A spokesman for the Kabul police chief said the bomber was stopped at the checkpoint near the gathering when he detonated explosives. Mujahid claimed the Taliban had inflicted a far higher number of casualties, but the insurgents often exaggerate their claims.
However, there has been no let up in the violence that has been killing and wounding more than 10,000 civilians a year - and many more combatants - with fighting continuing across large parts of the country and Kabul itself hit repeatedly by attacks.
The group has not publicly responded to Ghani's invitation and previously said it would negotiate only with USA officials.
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"Under his leadership, the TTP has also claimed responsibility for the December 16, 2014, attack on a school in Peshawar, Pakistan in which gunmen killed 148 people, including 132 students".
The death toll has risen to nine, Waheed Majroh, spokesman for the Health Ministry said.
Yamamoto stressed that President Ashraf Ghani "offered peace to the Taliban without preconditions, and laid out a path for negotiations with ... concrete proposals".
The overnight Taliban attack in northern Takhar Province took place in a remote region of the district of Khwaja Ghar.
The spokesman for the Pakistani Taliban says the son of their chief, Mullah Fazlullah, was among 21 "holy warriors" killed this week when missiles fired by a USA drone struck a seminary in Afghanistan. The report could not be independently confirmed because of the area's remoteness.
Security personnel carry human remains at the site of a suicide attack in Kabul. Another five officers were wounded in the gunbattle, he said.