Senior Taliban officials told NHK they have complied with the peace agreement and called on the Afghan government to promptly do its part.
As the ceasefire commenced, hundreds of worshippers went to mosques across the capital where they were patted down by armed guards before going inside.
The Taliban celebrate ceasefire in Ghanikhel district of Nangarhar province, Afghanistan, June 16, 2018.
At least 18 people, including Afghan security forces personnel, were killed in a suspected car-bombing in eastern Afghanistan on Thursday (July 30), hours before a three-day ceasefire was to begin in the country for the Muslim festival of Eid al-Adha, officials said.
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"To show goodwill and accelerate the peace talks, we will release 500 Taliban prisoners in response to the group's three-day ceasefire announcement", Ghani said in an Eid address.
There was no immediate claim of responsibility for the attack.
"The Secretary-General welcomes the announcement by the Government of Afghanistan and the Taliban of a ceasefire to enable the Afghan people to celebrate the Eid al-Adha holiday in peace", said a statement issued by the United Nations on Thursday.
"I do not have the right to decide on the release of those 400 Taliban prisoners who are accused of serious crimes", Ghani said, adding that a gathering of Afghan elders would decide their fate.
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The halt in fighting is slated to last for the duration of Id and is only the third official truce in almost 19 years of war. But that date passed amid political disarray in Kabul and disagreements over the prisoner exchange, with Afghan authorities saying some of the released Taliban inmates were returning to the battlefield.
Just months after the US signed a controversial deal with the Taliban to end the long-running war in Afghanistan - predicated on the notion that the insurgent group would not offer safe haven to Al Qaeda - local officials worry that terrorists still reign in parts of the country.
There are hopes of a permanent truce but peace talks have been delayed due to prisoner exchanges.
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