In the contested district of Bati Kot in Nangarhar, Taliban fighters carrying assault weapons and rocket-propelled grenade launchers traveled by vehicle and motorbike, waving Afghan and Taliban flags.
"The consequences could be disastrous", he said.
Attaullah Khogyani, spokesman for the provincial governor of Nangarhar, confirmed a auto bomb was responsible for the attack in the town of Ghazi Aminullah Khan, on the main Torkham-Jalalabad road.
A vehicle bomb killed at least 26 people at a gathering of Taliban and Afghan armed forces in the eastern city of Nangarhar on Saturday, an official said, as soldiers and militants elsewhere in the country celebrated an unprecedented ceasefire.
The only time direct talks between the Afghan government and the Taliban have been held, in 2015, they broke down nearly immediately.
No group immediately claimed responsibility.
However, a Defence Ministry spokesman, Mohmmad Radmanish, told dpa that "Taliban are allowed in and have visited cities, including the capital, Kabul, during the truce to celebrate Eid days with their families and friends".
Taliban members were similarly moved. ".Our normal operations will start tomorrow (Monday)".
"(That's) no bad thing if they are able to see the benefits of talking not fighting", he said.
Ghani said the current ceasefire will be extended from the fourth day of Eid.
Attaullah Khogyani, a spokesman for the Nangarhar governor, told RFE/RL that at least 54 others were also injured in the explosion.
Nangarhar Province is the main base of IS militants in Afghanistan. "Nobody has any clue how many Taliban militants are now hiding in civilian areas".
Afghan media outlets such as television stations ToloNews and Ariana News showed Interior Minister Wais Ahmad Barmak allegedly meeting Taliban militants in the eastern Kabul neighbourhood of Company.
In August, U.S. President Donald Trump unveiled a more hawkish military approach to Afghanistan, including a surge in air strikes, aimed at forcing the Taliban to the negotiating table.
As President Ghani emphasized in his statement to the Afghan people, peace talks by necessity would include a discussion of the role of global actors and forces.
The cease-fire does not include al Qaeda or the Islamic State group. But they have refused to meet with the United States-backed government, saying they will only negotiate with the U.S. directly.
"If they extend the ceasefire they will be compelled to talk, which I think the Taliban isn't interested in".
But Afghanistan has been at war for four decades, ever since the Soviet invasion in 1979.
Mumbai attack mastermind Hafiz Saeed on Saturday led Id-ul-Fitr prayers at the Qaddafi Stadium at Lahore amid high security even though the Pakistan government has outlawed his organisation Jamaat-ud-Dawah (JuD).
Early this month, more than 2,000 Afghan religious scholars from around the country issued a fatwa, an Islamic directive, saying "the ongoing war in Afghanistan is forbidden under Islamic law".
The death toll from a suicide bombing against a gathering of Taliban fighters in Afghanistan has risen to 36, an official said on Sunday.