After 12 years of violence in Afghanistan since the Taliban were ousted from power, pressure is growing for regional powers such as Iran, Pakistan and India to support a peace deal before 100,000 US-led foreign troops withdraw next year.
"Some while ago a delegation headed by the Islamic Emirate's political office chief had a three-day visit to Iran's capital, Tehran," the Taliban said in an emailed statement using the group's formal title.
No further details were given about who the Taliban met in Tehran or the exact dates or purpose of the visit, which was the first known trip by insurgent representatives to Iran.
A separate Taliban group also made another visit to Iran to attend a conference, the statement said.
Iran, which has strong trade ties with western Afghanistan, has been affected by unrest in Afghanistan, with hundreds of thousands of refugees crossing the border to escape the war.
Efforts to start peace talks between the Taliban and the Afghan government have failed. The insurgents refuse to talk to President Hamid Karzai, whom they describe as a puppet of the United States.