But the group warned the suspension of fighting for the first three days of Eid, the holiday that caps off Ramadan, did not extend to "foreign occupiers", who would continue to be targeted by the militants.
The Afghan government says the ceasefire will last for a week and will exclude Daesh and other terror groups.
"Only three days the Taliban are not killing us".
A statement released Saturday by the Taliban said that they would defend themselves in case of any attack.
However, U.S. -led North Atlantic Treaty Organisation forces are exempt from the ceasefire, with the Taliban saying they would continue to attack "foreign invaders", the Wall Street Journal reported.
"With the ceasefire announcement, we epitomise the strength of the Afghan government and the will of the people for a peaceful resolution to the Afghan conflict", he added.
The move came days after a gathering of Afghanistan's top clerics in Kabul called for a ceasefire and issued a fatwa against suicide bombings and attacks.
No one immediately claimed the attack in Kot district, but both the Taliban and IS are active in eastern Afghanistan, especially in Nangarhar.
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In its statement, the Afghan Taliban said it would allow prisoners to visit with families and asked for the group's regional leaders to commute some prisoners' sentences.
The US and North Atlantic Treaty Organisation formally concluded their combat mission in Afghanistan in 2014, but the US still has thousands of forces based there in a support and counterterrorism role.
Laurel Miller, who served as a senior USA official for Afghanistan and Pakistan under both Obama and Trump, said that while any action to reduce violence was positive, the differing terms and timelines for the two parties' cease-fires made the current circumstance a fragile one.
The US state department said its forces and coalition partners in Afghanistan would "honour the ceasefire".
While the Taliban announced it would halt attacks in response to Ghani's truce offer, it considers his government to be illegitimate and has said it would only hold peace talks with the United States. He added that eight insurgents were killed and more than a dozen others were wounded in the gun battle in Zewal district.
Still, Taliban spokesman Zabihullah Mujahid told the Times that Saturday's announcement of Taliban cease-fire was unrelated to the government's actions.
Last month, the Pentagon said that senior Taliban officials have been secretly negotiating with Afghan officials on a possible ceasefire.
Qureshi further added that at least nine Taliban insurgents were also wounded during the clashes with the security personnel.