The remarks come after Iran confirmed Monday that the Taliban had visited Tehran for a second round of talks in just a few days that are aimed at ending the 17-year conflict, AFP reported.
The Taliban delegation on Sunday discussed with Iran "the post-occupation situation, restoration of peace and security in Afghanistan and the region", the militant group said in a statement posted on social media and emailed to journalists.
It signals a growing confidence among the Taliban for US troops to pull out of Afghanistan, after US officials last month told various media outlets that President Donald Trump had decided to slash "roughly half" of the 14,000 US boots on the ground.
Iranian Foreign Ministry spokesman Bahram Qassemi said at a televised news conference that the talks were held with the knowledge of Afghan President Ashraf Ghani.
Qassemi said Iran's priority was "to help facilitate negotiations between Afghan groups and the country's government."
"Considering our long border with Afghanistan and the cultural and historical ties, and our important role in the region's stability, the Islamic Republic was interested... to enter and play a more important role in peace development in Afghanistan," he added.
Iran's Deputy Foreign Ministry Abbas Araqchi will travel to Afghanistan in the next two weeks for further talks, the Foreign Ministry said without giving further details.
The Taliban also met with the United States, Pakistan and Saudi Arabia in the United Arab Emirates earlier in December as part of a flurry of diplomatic efforts to end the war.
But the Taliban refused to meet a delegation from Afghanistan. The militant group said Saturday its representatives would not meet "with those of the Kabul administration" at the next meeting expected to be held in Saudi Arabia later this month.
Iran and Afghanistan share a 950-kilometer (580-mile) border, and have had a complex relationship in recent years.
Iran worked alongside the United States and Western powers to help drive out the Taliban after the US-led invasion in 2001.
In 1998, Iran held the Taliban responsible for the deaths of nine Iranian diplomats who were working in its consulate in northern Afghanistan and sent reinforcements to the long border that Iran and Afghanistan share.