The Taliban say one of their soldiers was killed in Sunday’s fighting, which occurred in the border area between Afghanistan’s Nimroz province and Iran’s Hirmand region.
Each country blamed the other for the incident.
There have been several clashes at the border since Taliban militants took over Afghanistan a year ago.
The exact circumstances of the latest skirmish are unclear.
“We have one killed and one wounded,” Nimroz police spokesman Bahram Haqmal told Reuters news agency.
In Iran’s Sistan va Baluchestan province, Hirmand official Maysam Barazandeh was quoted by Fars news agency as saying there had been no casualties on the Iranian side.
Iran’s Tasnim news agency said the fighting broke out after Taliban forces tried to raise their flag “in an area which is not Afghan territory”, leading to an exchange of gunfire lasting “several minutes”.
“Our forces gave the necessary response,” Mr Barazandeh said.
Last month Iran’s foreign ministry reported the death of an Iranian border guard following another incident in the same area.
