The delegation comprises Shahabudin Delawar, Mullah Fazil and Khairkhwa Khairullah, three senior members of the Taliban based in Qatar.
Syed Akbar Agha, a former Taliban member, said that a ceasefire between the Taliban and the Afghan government is dependent on the signing of a deal and withdrawal of foreign troops from Afghanistan.
US negotiator Zalmay Khalilzad resumed talks with the Taliban earlier this month, three months after President Donald Trump halted them citing a deadly attack in Kabul.
As talks were ongoing in Doha, the Taliban carried out a suicide attack targeting Bagram air base, which killed two civilians and wounded dozens others.
On December 13, Khalilzad said that they were taking a brief pause for the Taliban to consult their leadership on ceasefire.
“Taliban must show they are willing and able to respond to Afghan desire for peace,” Khalilzad said.
Latif Mahmud, deputy spokesman for Afghan president, said that clearing of relations between the Taliban and Pakistan would itself facilitate peace talks between the Afghan government and the Taliban.
Najia Anwari, spokesperson for Afghan State Ministry for Peace Affairs, said that the Taliban should not ignore opportunities for peace talks with the Afghan government.