While the source said the attack happened near the Governor's Palace, or the Shahi Palace, where civil servants and Taliban insurgents were meeting to discuss the ceasefire, Khogyani said that the attack was an at area where there were only civilians.
No one immediately claimed the attack, but it was likely carried out by Daesh (also known as ISIL or ISIS), which was not included in the ceasefire and has clashed with the Taliban in the past.
Meanwhile, Taliban fighters in Helmand have said that the Taliban are also exhausted of war.
Speaking on condition of anonymity, the Taliban official also said Pakistan had wanted the Taliban to include USA and other foreign troops in the ceasefire, but the Taliban's leadership and supreme commander, Sheikh Haibatullah Akhunzada, did not agree.
But later Sunday, the Taliban announced that their cease-fire had ended and they had no intention of extending it.
He made no reference to Ghani's announcement.
In extraordinary scenes during Eid al-Fitr, the end of the holy fasting month of Ramadan on Saturday, militants embraced security force members and took selfies with citizens.
The Taliban attacked in the Afghan provinces of Helmand and Kandahar as night fell.
In a statement released late on Saturday, Qassemi sympathized the Afghan people and government over the deadly attack targeting Afghan and Taliban forces in the eastern city of Nangarhar.
But the Islamist group said its own three-day ceasefire would end at midnight on Sunday evening as planned.
"The Government's extension of the ceasefire provides a clear opportunity for initiating a negotiated solution to the conflict", said Tadamichi Yamamoto, the United Nations secretary general's special representative for Afghanistan.
The Afghan government and the Taliban for the first time in more than 17 years mutual observed the cease-fire that had gone into effect on Friday, the opening day of the three-day Eid festival. They would, however, continue attacking US-led North Atlantic Treaty Organisation troops.
President Ghani reiterated his offer of direct talks with the Taliban to resolve mutual differences and end the conflict.
Millions of Afghans celebrated the cease-fire and Eid over the weekend as Taliban militants and government officials displayed surreal expressions of brotherhood. The Alliance still maintains a presence to train Afghan forces there.
Taliban fighters, security forces and civilians were also targeted during cease-fire celebrations Saturday in Nangarhar's Rodat district. The Taliban had already denied involvement.
"During the cease-fire, we will provide medical assistance to the wounded Taliban, and will provide them any humanitarian assistance if needed", Ghani said on Twitter.