"Unfortunately, about 20 people - including civilians and Afghan Taliban members who were celebrating a cease-fire - were killed in the attack and around 16 other people were injured", Khogyani said.
On Sunday, Taliban insurgents were travelling freely with their flags and meeting civilians despite curbs imposed after the Nangarhar attack.
Earlier in the day, dozens of unarmed Taliban fighters entered the Afghan capital to celebrate Eid.
Hardened Taliban fighters and Afghan security forces hugged it out during a three-day ceasefire called to mark Eid al-Fitr, the Muslim holiday that ends the holy month of Ramadan.
In his conversation with Mr. Ghani, Mr. Mulk said that Fazlullah's death would be received throughout Pakistan with relief as Pakistanis had borne the brunt of terrorist attacks by the Tehrik-e-Taliban Pakistan, which Fazlullah headed.
The Taliban are fighting USA -led North Atlantic Treaty Organisation forces, combined under the Resolute Support mission, and the US -backed government to restore sharia, or Islamic law, after their ouster by US -led forces in 2001.
The president said many were skeptical about Taliban's positive response to the ceasefire before it was put into practice, but all those doubts vanished once the ceasefire went into effect and assumptions made by many analysts and politicians proved wrong.
The Taliban are fighting US -led North Atlantic Treaty Organisation forces, combined under the Resolute Support mission, and Ghani's USA -backed government to restore sharia, or Islamic law, after their ouster by US -led forces in 2001.
Alleged Taliban members meet and greet Afghan people on Saturday. STR
Western diplomats based in Kabul said they were issuing fresh travel warnings for the whole country.
"The United States is prepared to support, facilitate, and participate in these discussions", Pompeo said in a statement. He said there had been an "exchange of views" between the government and the Taliban over the past week, without elaborating.
Provincial police spokesman Shahpur Ahmadzai told The Associated Press that the Taliban were unarmed and no one was allowed into the city with weapons.
Ghani´s extension of the government´s eight-day ceasefire, which had been due to expire Tuesday night, drew immediate worldwide support and calls for the Taliban to follow suit. For many Afghans it has been first glimpse of peace in their lifetime. For the first time, we felt safe.
Trump also pledged to support Afghan troops in their war against the Taliban and maintain American presence in the country for as long as there was a need for it.
They said they would continue attacking US-led North Atlantic Treaty Organisation troops. It is hard to describe the joy, ' said student Qais Liwal.
"I could not believe my eyes", he told Reuters. "I was very surprised when I saw Taliban and security forces posing together for pictures".
Photos on news websites showed armed police standing in line at the corner of the street hugging Taliban fighters one by one.
A video showed huge crowd of people screaming and whistling as they welcomed the Taliban. He did not give details about how long he expects it to last.