Afghan security forces say the impact has been significant, but the Taliban roam huge swaths of the country and, with foreign troop levels of about 15,600, down from 140,000 in 2014, there appears little hope of outright victory.
"We welcome the three days ceasefire announced by the Taliban starting on the first day of Eid".
The surprise move by the government came days after a gathering of Afghanistan's top religious leaders in the capital, Kabul, issued a fatwa - a religious edict issued by an expert in Islamic law - against suicide bombings and attacks.
The Taliban had denounced the gathering, insisting its fight against what it considers are foreign invaders was justified.
'Our operations will continue against them, we will attack them wherever we see them, ' it said. "We should reach for sustainable peace throughout the country".
President Ashraf Ghani on Thursday declared an apparently unilateral week-long ceasefire with the Taliban.
The ceasefire from the Afghan government's side is applicable from 27th of Ramadan, June 12, to the fifth of Eid-al-Fitr, June 19.
Still, Taliban spokesman Zabihullah Mujahid told the Times that Saturday's announcement of Taliban cease-fire was unrelated to the government's actions.More news: Rashford shines as England cruise past Costa Rica
In late February, Ghani also offered the Taliban a chance to be recognized as a legitimate political party and withdraw their names from global sanctions lists in exchange for peace.
The UN secretary-general's special representative for Afghanistan, Tadamichi Yamamoto, said he hoped the ceasefires would "serve as a stepping stone" towards peace talks between the Afghan government and the Taliban.
An Afghan security force member stands guard in front of the Marshal Fahim military academy in Kabul, Afghanistan January 29, 2018. It is underpinned both by the heavy daily toll of the long war on ordinary Afghans and U.S. President Donald Trump's limited patience for the costly U.S. involvement here.
In February, Ghani offered recognition of the Taliban as a legitimate political group in a proposed political process that he said could lead to talks to end more than 16 years of war.
The Islamist insurgency has inflicted heavy casualties on Afghan forces since launching its spring offensive in April and reportedly killed around 500 personnel last month.
At least 50 Afghan soldiers and police were killed in clashes across the country - 17 soldiers died in the Zawal district of western Herat province, nine border police were killed in the Bala Murghab district of north-western Badghis province, and at least 20 Afghan police were killed in the Qala e Zal district of northern Kunduz province on Friday.
Ghani proposed a ceasefire and a release of prisoners among options including new elections involving the militants and a constitutional review in a pact with the Taliban to end a conflict that a year ago alone killed or wounded more than 10,000 civilians.