According to the militants, one of their members was killed during a battle on Sunday in the region where Nimroz province in Afghanistan and Hirmand in Iran meet.
Since the Taliban took over Afghanistan a year ago, this incident—the most recent—has been placed on both countries by the other.
Last month Iran reported the death of one of its guards in an incident in the same area.
The details of the most recent clash are unclear, but according to an Iranian account, the Taliban forces attempted to hoist their flag on non-Afghan soil when the firing began.
No casualties were recorded on the Iranian side.