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.
