File Photo: Taliban foreign minister Amir Khan Muttaqi. (AFP)
Iran, like other nations, has so far not recognised the new government formed by the Taliban after it took power amid a hasty withdrawal by US-led foreign forces in August.
"The visit aims at discussions on political, economic, transit and refugee issues between Afghanistan and Iran," the Taliban foreign ministry spokesman Abdul Qahar Balkhi said on Twitter.
Already host to millions of Afghans and fearing a new influx, Tehran has sought to sketch a rapprochement with the Taliban.
The Taliban delegation led by Foreign Minister Amir Khan Muttaqi has already held a preliminary meeting with Iranian officials, he said.
Shiite Iran, which shares a 900-kilometre (550-mile) border with Afghanistan, had not recognised the Sunni movement's rule during their 1996 to 2001 stint in power.
It is still to recognise the Islamists' current government, insisting that the Taliban form an inclusive administration.
"Today, we are basically not at the point of recognising" the Taliban, Iranian foreign ministry spokesman Saeed Khatibzadeh told a news conference earlier this week.
The Taliban has formed an all-male cabinet made up entirely of members of the group, and almost exclusively of ethnic Pashtuns.
It has further restricted women's rights to work and study, triggering widespread international condemnation.