The militants say one of their fighters was killed in Sunday’s fighting in the border area between Nimroz province in Afghanistan and Hirmand in Iran.
Each country blamed the other for the incident, the latest since the Taliban overran Afghanistan a year ago.
Last month Iran reported the death of one of its guards in an incident in the same area.
The exact circumstances of the latest skirmish are unclear but one Iranian report says shooting started when Taliban forces tried to raise their flag on non-Afghan territory.
There were reportedly no casualties on the Iranian side.
