Two Afghan Taliban officials confirmed that three of the group's leaders - believed to be drawn from a negotiating team based in Qatar - are holding talks with Iranian officials, The Express Tribune reported.
"The Taliban will explain their policies and will allay the fears of Iran as it always had concerns about Taliban being Sunnis," said one Taliban official who did not wish to be identified.
Syed Tayyeb Agha, Maulvi Shahabuddin Dilawar and Sher Muhammad Abbas Stanakzai are part of the delegation visiting Iran.
They began the visit on Friday after approval by the top leadership of the Afghan Taliban.
This is the first high-level and formal interaction between the two sides, the Taliban officials said.
It is believed that Iran extended an invitation to the Afghan Taliban in order to have a role in any future process ahead of the 2014 endgame in Afghanistan.