The government says it will continue a unilateral ceasefire for another 10 days, although security forces can defend themselves if attacked, a BBC report said.
There were unprecedented scenes of soldiers and Taliban insurgents hugging each other during the ceasefire.
But the ceasefire failed to end violence entirely.
At least 18 people were killed in a suicide attack in the city of Jalalabad, outside the office of the Governor of Nangarhar province while officials were meeting Taliban insurgents. Dozens were injured.
No group said it carried out the attack.
On Saturday a suicide bombing in the same province, also on a gathering of Taliban and local officials, left 36 people dead. The Islamic State group said it carried out that attack.
The militants said there would be no extension to the ceasefire and fighters would be expected to leave government-controlled areas before sunset.
In a statement, the Taliban said it had called the ceasefire to enable ordinary Afghans to enjoy a peaceful Eid, "not in response to the ceasefire of the Kabul regime".
The group hailed the success of the ceasefire as a sign of its cohesion, and reasserted its determination to seek the "withdrawal of foreign invaders and establishment of an Islamic government".
President Ashraf Ghani's plea on Saturday for the Taliban to prolong its truce has been rejected.
His office said on Sunday that the government's extended truce would still allow Afghan security forces to "defend themselves against any attack".
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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