The semiofficial Fars news agency quoted local judicial official Mohammad Marzieh as saying that the 16 were executed today, hours after the rebels ambushed the border guards near the town of Saravan in southeast Iran.
Drug smugglers have occasionally ambushed Iranian troops in the area.
Ethnic Baluch armed groups also operate there, but recently have been much less active.
The report provided few other details. It did not mention a trial, suggesting the prisoners may already have been convicted and sentenced to death, and their executions moved up after the ambush.