The ceasefire which begins Sunday was first announced by the Taliban, then welcomed by Afghan President Ashraf Ghani.
Eradicating terror from Afghanistan remains the top priority, but all sides must now agree on methods.
Taliban, which denied involvement in Tuesday's attacks that killed over 50 people, says it is "fully prepared" to counter any strikes ordered by Afghan President Ashraf Ghani.
Spokesman Zabihullah Mujahid said the group would not negotiate with the team as it was not selected in a way that included "all Afghan factions".
Afghanistan's perennial runner-up will not be content with second place this time.
President Ashraf Ghani orders release of initial 1,500, with other 3,500 fighters to be set free in parallel with progress in intra-Afghan talks. Taliban says the plan violates its peace deal with US.
Top US negotiator, Zalmay Khalilzad is known to have connections with shadowy figures in Afghanistan and experts are struggling to understand what exactly he has agreed with the Taliban.
Hundreds of people had assembled at two venues inside the presidential palace complex to watch the swearing-in ceremonies for President Ashraf Ghani and challenger Abdullah Abdullah, when the blasts were heard.
Threat of parallel governments in Afghanistan is jeopardising the nascent process to end a war that has killed tens of thousands of people.
Election commission declares incumbent Ashraf Ghani winner of disputed presidential election held almost five months ago, but rivals say commission and outcome "have no legitimacy."
The negotiations appear to give the Taliban some degree of political legitimacy in Afghanistan following the complete withdrawal of US forces and in exchange the insurgent group is expected to stop harbouring 'terrorists'.
An escalated conflict between the US and Iran will reverberate in Pakistan and Afghanistan.
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