The Iranian News Agency said the incidents took place in the city of Dahlaran, on the Iran-Iraq border, also wounding two people.
In the first incident two sheepherders stepped on a landmine, which exploded, mutilating their bodies and killing them instantly.
An Iranian soldier was killed and two others wounded in another mine explosion while clearing a minefield in the border province of Eilam where as many as 50 people have been killed in mine blasts during the current year.