Nusrat Rahimi, deputy spokesman for Interior Ministry, told Anadolu Agency the suspected bomber detonated his explosives at a security barrier in the Dasht-e-Barchi neighborhood in western Kabul.
Among the dead were two policemen, he said. Officials said the attacker was on foot.
The most lethal suicide bombing against Hazaras came in 2016, killing more than 80 people.More news: Clocks move ahead one hour overnight Saturday
At least seven people have been killed and seven others wounded after a suicide attack near a Shia mosque in the Afghan capital, Kabul, officials said.
The overnight Taliban attack in northern Takhar Province took place in a remote region of the district of Khwaja Ghar.
On February 28, Ghani offered to allow the Taliban to establish itself as a political party and said he would work to remove sanctions on the militant group, among other incentives, if it joined the government in peace negotiations.More news: Russian Federation won't accept meddling in its domestic affairs - Putin
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.
Ten local policemen were killed and nine were wounded in the ambush, provincial police spokesperson Khali Aseir said.
Ghani at an global conference in Kabul last week unveiled a plan to open talks with the Taliban, including eventually recognizing them as a political party. "These attacks are a blow to the president's efforts to hold talks with the Taliban and a clear signal that they reject his offer".More news: Active Shooter Confirmed at Yountville Veteran's Home in Napa County
Wells, who is leading the Afghan peace effort for the USA government, said Washington was supporting talks without preconditions to allow for "creative solutions and approaches".