An Afghan security force member stands guard in front of the Marshal Fahim military academy in Kabul, Afghanistan January 29, 2018.
It's the first time the militants have made such an offer, which comes days after the government declared its own ceasefire. It is also not clear when the ceasefire would take effect.
But it added that 'if the mujahideen are attacked we will strongly defend (ourselves)'.
However, the Taliban said the ceasefire did not include cessation of hostilities against foreign troops, Tolo News reported.
"The reason for announcing it this time is that, after the Kabul administration announced theirs, the people were concerned that our Mujahedeen might continue operations and it might disturb their Eid celebrations", Mujahid said.
The issue has reportedly undermined the Afghan forces capability to fight the Taliban and other terrorist groups.
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Despite the increasing intensity of conflict in Kabul and around the country, Afghans remain hopeful that the ceasefire will bring much needed relief in an otherwise intensifying war.
Although the Taliban statement did not acknowledge the government cease-fire, the moves by the two sides would overlap for three days.
The Trump administration has increased the number of US troops in Afghanistan in an effort to give local forces, which continue to struggle despite more than a decade and a half of outside support, a battlefield advantage.
All the deaths were claimed by the Taliban.
In February Ghani unveiled a plan to open peace talks with the Taliban, including eventually recognizing them as a political party. Mattis spoke to reporters during a break in a North Atlantic Treaty Organisation defense ministers meeting. Just hours before the Taliban's announcement, at least 17 soldiers were killed when their checkpoint came under attack by Taliban fighters in western Herat province, said Gelani Farhad, spokesman for the provincial governor.
Some diplomats said it came as a bit of a surprise, showing that at one level the government wanted intensified air strikes, but on another it was offering an olive branch.
Ghani proposed a ceasefire and a release of prisoners among a range of options including new elections involving the armed group, and a constitutional review in a pact with the Taliban to end a conflict that previous year alone killed or wounded more than 10,000 Afghan civilians. He added that eight insurgents were killed and more than a dozen others were wounded in the gun battle in Zewal district.
Qureshi further added that at least nine Taliban insurgents were also wounded during the clashes with the security personnel.