According to Nasrat Rahimi, deputy spokesman for the interior minister, a suicide bomber blew himself up while trying to enter a gathering commemorating the anniversary of the death of Abdul Ali Mazari, a former leader of the mainly Shia Hazara community.
Amin said the bomber detonated his explosive device at a checkpoint "after being identified by police".
President Mohammad Ashraf Ghani called the attack a crime against humanity. One policeman was among the dead.
His confirmation came a day after officials said the drone targeted a compound, and Khurasani said those killed in the strike were seminary students.
Fazlullah is the leader of Tehrik-e-Taliban Pakistan said to be responsible for numerous terrorist acts against Pakistani and US interests including a failed attempt to detonate an explosive device in New York's Times Square in 2010.More news: Thomasville Fire Rescue offers free smoke detectors
The spokesman for the Health Ministry, Wahid Majro, said several of the wounded were in critical condition and feared the death toll could rise further.
Ten local policemen were killed and nine were wounded in the ambush, provincial police spokesperson Khali Aseir said.
"We are in Afghanistan as a guest of a sovereign Afghan government that's recognized by the United Nations and global community, with our presence enshrined in the strategic partnership agreement and a bilateral security agreement".
In other developments, the Taliban launched a deadly assault overnight on an army outpost in a remote region of northern Takhar province, killing six soldiers and wounding five, Defense Ministry spokesman Dawlat Waziri said.
Tadamichi Yamamoto told the Security Council Thursday the Taliban's argument that it won't talk to the government because the conflict is not between Afghan parties "misrepresents the reality".