According to the Taliban, one of their troops was killed in Sunday's combat in the border region between the Afghan province of Nimroz and the Iranian province of Hirmand.
Each nation held the other responsible for the incident.
Since the Taliban gained control of Afghanistan a year ago, there have been several border conflicts. The circumstances surrounding the most recent conflict are murky.
Bahram Haqmal, a police spokesman for Nimroz, told the Reuters news agency, "We have one fatality and one injury."
Maysam Barazandeh, a Hirmand official in Iran's Sistan va Baluchestan region, was quoted by the Fars news agency as stating there were no Iranian injuries.
According to Iran's Tasnim news agency, combat broke out as Taliban fighters attempted to fly their flag "in an area that is not Afghan territory," resulting in "several minutes" of shooting.
"Our forces responded appropriately," said Mr. Barazandeh.
The Iranian foreign ministry confirmed the death of an Iranian border guard in the same region one month ago.