At least 9 people have died in an attack targeting the military in Helmand province.
The discussions are part of a drawn-out process and a quick breakthrough on thorny issues is unlikely.
The attack happened hours before a three-day ceasefire was to begin. The Taliban denied any responsibility.
The offer from the militants comes amid soaring violence that has threatened to derail US-backed efforts to bring Kabul and the Taliban to the negotiating table and seek an end to Afghanistan's nearly 19-year war.
Meanwhile, the US has said its deal with the Taliban is in the "next phase" as it urged the militants to reduce rising bloodshed.
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.
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