The incoming president should make America's longest war his first foreign policy priority.
While officials have been jubilant over an agreement between the two sides, a lot more needs to be done to end the cycle of violence.
The meeting comes a day after Kabul and the Taliban reached a preliminary deal to move ahead with dialogue.
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".
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