The Taliban had already denied involvement.
Almost 70 people were killed or wounded after a suicide bomber detonated his explosives near the governor's compound in Jalalabad city city at around 3 pm local time.
There was no immediate claim of responsibility for the blast that also wounded at least 16 others marking the suspension of fighting in Rodat district of Nangarhar province, but an Afghan security source told AFP that the Daesh terrorist group was to blame.
"The enemy has misused the ceasefire issue and there is a chance of more such bad incidents happening", Mujahid said in an earlier message.
The bomber targeted a gathering of fighters who were celebrating a three-day truce coinciding with the Eidul Fitr holiday.
The chairman of the High Peace Council, a government body charged with negotiating an end to the almost 17-year war, called on the Taliban to accept the extended cease-fire and join the peace process.
Mulk made the comment in a telephone conversation Friday night with Afghan President Ashraf Ghani and thanked him for sharing information about Fazlullah's killing, said a Pakistan government statement.
The unprecedented scenes come during the overlap between dual ceasefires declared by the Afghan Government and the Taliban to mark Eid, the celebration at end of the Islamic holy month of Ramadan.
U.S. Secretary of State Mike Pompeo, echoing Ghani's announcement on Saturday, said peace talks would have to include a discussion on the role of "international actors and forces".
A senior Western diplomat in Kabul earlier said Ghani's decision was "a bold move" but questioned what happens if the Taliban do not extend their halt in hostilities against government forces.
The Taliban are fighting US -led North Atlantic Treaty Organisation forces, combined under the Resolute Support mission, and the USA -backed government to restore sharia, or Islamic law, after they were ousted by USA -led forces in 2001. Traffic jams formed where people stopped to take pictures of the fighters with their flags.
One image even showed an Afghan general leaving his auto to have selfies taken with an enthusiastic group of Taliban fighters. Their weapons would be returned when they leave, he said.
But over the past two days Taliban fighters could be seen celebrating the truce alongside Afghan troops and other people in a number of locations.
Meanwhile, videos and photos posted on news sites and social media showed soldiers and Taliban greeting and hugging each other and taking selfies in several provinces. Some people were dancing and clapping as onlookers took photos with their smartphones.
Over the weekend, ecstatic men and children crowded around the soldiers and Taliban fighters, some of whom had checked in their weapons at the entrances to cities, and urged them to turn their ceasefire into a permanent peace.
"It was the most peaceful Eid", said Qais Liwal, a student in Zabul, a city in country's south. "I felt for the first time in the eight years of my jihadist life that I am at least safe".