Their announcement came days after the Afghan government declared a unilateral eight-day ceasefire, and for the first time it promised Afghan civilians, who have borne the brunt of the 17-year conflict, a temporary reduction in violence, which has only been getting worse in recent years.
The Taliban also said it may release prisoners including government troops, provided they agree to refrain from fighting insurgents in the future, the statement said. The Taliban has announced a three-day ceasefire over the Eid holiday. "Let us hope peace prevails", he said. Omar Zakhilwal, Afghanistan's Ambassador to neighboring Pakistan, described the announcement as an "important step towards prospects for peace".
Defense Secretary Jim Mattis said this could, for example, allow the U.S.to partially shift the focus of aerial surveillance from the Taliban to IS fighters as well as al-Qaida extremists, who remain a threat 17 years after the USA invaded.
Ghani first spoke about the possibility of a ceasefire with the militant Islamist group in February, when he announced that the Afghan government was willing to recognize the Taliban as a legitimate political party as part of a potential agreement.
Eid is the biggest festival in the Muslim calendar when families visit each other's homes, enjoy feasting and in Afghanistan tend graves of fallen loved ones.
USA officials said Thursday that the Taliban had expressed interest in the pause in hostilities through Pakistani back channels and other mechanisms. The festival lasts up to three days. "If different factions don't accept the ceasefire, then attacks will continue".
North Atlantic Treaty Organisation has led worldwide security efforts in Afghanistan since 2003.
In a televised address on Thursday, Afghan President Ashraf Ghani announced an unconditional ceasefire with the Taliban until June 20, coinciding with the end of fasting month of Ramadan.
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.
The clerics also recommended a ceasefire with the Taliban and Ghani endorsed the recommendation.
In late February, Ghani also offered the Taliban a chance to be recognized as a legitimate political party and withdraw their names from worldwide sanctions lists in exchange for peace.
The proposed cease-fire offers Afghanistan's High Peace Council hope for negotiating peace with the Taliban.
Afghan security officials on Saturday said in the past 24 hours the Afghan National Defense and Security Forces (ANDSF), Taliban and Daesh suffered heavy losses in battles in a number of provinces.
The Taliban's surprise announcement comes as Trump and North Korean leader Kim Jong Un are due to sit down to a summit in Singapore on Tuesday, something few people would have predicted just months ago when threats between the two sides were at their most bellicose.