A statement released Saturday by the Taliban said that they would defend themselves in case of any attack.
Afghan officials say Taliban militants have killed over 40 government security personnel in attacks across the country. The Taliban said it was not behind the attack, but described the meeting as "a USA effort".
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 Daesh fighters as well as al-Qaida extremists, who remain a threat 17 years after the USA invaded.
But the group said its attacks against US-led troops stationed in the country will continue unabatedly in any area.
His offer comes amid a rise in attacks by the insurgents, who have gained ground in recent months despite a surge in ground and aerial offensives by USA and Afghan forces.
Speaking on the sidelines of a North Atlantic Treaty Organisation defence ministers' meeting in Brussels, Nicholson said United States forces would respect the apparently unilateral ceasefire with the Taliban announced by Afghan President Ashraf Ghani on Thursday.
Ghani's cease-fire offer did not cover Afghan operations against the Islamic State or other hard-line groups.
"We hope that (the Taliban) will be committed to implementing their announcement of the cease-fire", he said.
The Taliban attacked security outposts in the Zawul district of western Herat province on Friday night, killing 17 troops and wounding several, Jelani Farhad, spokesman for the provincial governor, said.
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 past year alone killed or wounded more than 10,000 civilians.
Ghani's surprise declaration came on the heels of a fatwa issued by Afghanistan's top clerics forbidding suicide attacks and a Pentagon announcement that senior Taliban officials had been negotiating with Afghan authorities on a possible ceasefire.
There was no immediate response to the Taliban's statement from the US military, which has a dual mission to support Afghan troops against the Taliban and, separately, conduct counterterrorism operations against extremists associated with the Islamic State and al-Qaeda.
"Twenty four local police and public uprising forces and 23 insurgents were killed in clashes", Kunduz police spokesman Anamuddin Rahmani said. "Insurgents have set fire to two military Humvees as well as the checkpoint", he said. "Afghans are under occupation and "jihad" is an obligation", Mujahid said when asked if the Taliban would prolong the truce period.
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