Provincial health director Najibullah Kamawal put the toll from Sunday's blast in Jalalabad city, outside the office of the Nangarhar provincial governor, at 18 dead and 49 wounded.
Tens of thousands of Afghans have been killed since the US-led invasion drove the Taliban from power in 2001.
He also urged the Taliban to extend their three-day ceasefire which is due to end Sunday.
Nangarhar provincial Police Chief Ghulam Sanayee Stanikzai said the devastating explosion came as previously unthinkable scenes of unarmed Taliban fighters celebrating Eid, often alongside Afghan security forces, played out in cities throughout the war-shattered country on Friday and again on Saturday.
No one immediately claimed responsibility for the attack, but ISIS has a strong presence in the region.
1 magnitude natural disaster shakes Japan; hundreds injured
Osaka officials did not give details, but the injuries reported in Kyoto and three other neighboring prefectures were all minor. Prime Minister Shinzo Abe told reporters the government was "working united, with its first priority on saving people's lives".
The Taliban's statement added that their cease-fire for their fighters to celebrate the holiday peacefully and not in response to the government's cease-fire announcement.
"Good steps for peace have been taken, but more steps have to be taken", said council chairman Karim Khalili.
Before the Taliban's ceasefire had even started, analysts had expressed cautious optimism that the truces, if successful, could help build trust between the government and the Taliban and lay the groundwork for peace talks.
Saturday was the second day of cease-fire declared by the Taliban and the fifth day of the cease-fire announced by the government.
Fazlullah was killed in Afghanistan's northeastern Kunar province.
In the meantime, the USA embassy said in a statement that the United States extends its best wishes to the people of Afghanistan in celebration of Eid al-Fitr.
Fazlullah, also known by the alias Radio Mullah or Maulana Radio due to his long sermons on a private radio channel, and his commanders were having an Iftar party at a compound when a remotely piloted U.S. aircraft targeted them, reports said.
Record-breaking Eid celebration in Birmingham
Fasting is completed with holiday of 'Eid al-Fitr.' On this day, it is required that all wealthy Muslims aid the less fortunate. During this period, Muslim faithful prayed, strived for spiritual growth, scarified and gave time and effort to those in need.
The TTP has claimed responsibility for several deadly attacks targeting civilians and security personnel alike in Pakistan including the December 16, 2014 Army Public School carnage that had killed 150 people including more than 130 children. "We are ready for comprehensive negotiation, all those issues and demands that have been put-forth we are ready to discuss them at the peace talks", Ghani said.
There were also festival-like scenes of rival fighters parading down city streets in Logar, holding Afghan and Taliban flags.
In a statement later Saturday, the US government and North Atlantic Treaty Organization forces in Afghanistan supported Mr. Ghani's extension of the cease-fire.
The only time direct talks between the Afghan government and Taliban have been held, in 2015, they broke down nearly immediately.
The government also released some Taliban prisoners, he said. "The United States is prepared to support, facilitate and participate in these discussions", the statement said.
American forces and NATO's non-combatant Resolute Support in Afghanistan welcomed an extension of the cease-fire by Ghani and his offer to begin peace talks with the Taliban.
Officials expect full containment of 416 Fire near end of July
Above: A photo of the 416 Fire uploaded to Inciweb around June 10, 2018. "We recognize the conditions are dry and hot", Gov. The order is effective Friday for the Mountainair and Sandia districts, and in place June 22 for the Mount Taylor district.