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.
USA forces said they would honour the Afghan government ceasefire.
"This ceasefire is an opportunity for Taliban to introspect that their violent campaign is not winning them hearts and minds but further alienating the Afghan people from their cause", Mr. Ghani said in a public statement.
But it added that 'if the mujahideen are attacked we will strongly defend (ourselves)'.
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President Ghani had ordered security forces to cease operations against the Taliban last week but stressed that the fight against the Islamic State, al-Qaida and other groups in the country would continue.
"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.
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.
A Taliban spokesman claimed its fighters killed 35 soldiers and captured six others besides seizing military vehicles and weapons. Each day a year ago, an average of about 28 Afghan police officers and army members were killed.
The Taliban's statement added that the leadership of the Taliban may also consider releasing prisoners of war, if they promise not to return to the battlefield.
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There was no immediate response to the Taliban's statement from the USA 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.
"This will continue and in fact will be intensified during the period of ceasefire", General John Nicholson, who commands USA and North Atlantic Treaty Organisation forces in Afghanistan, told reporters.
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Farhad said one soldier was wounded.
Ghani on Thursday, June 7, 2018 announced a weeklong cease-fire with the Taliban to coincide with the holiday.
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In northern Kunduz province at least 13 local policemen were killed early Saturday when their checkpoint came under an attack by Taliban fighters, said Nematullah Temori, spokesman for the provincial governor.