The first attack occurred in the city of Bent, Nik Shahr District, during which gunmen opened fire on participants in a school ceremony, killing the chairman of the city council, the commander of the Islamic Revolution Guards Corps in Bent, Parviz Kadkhodaei, and two soldiers.
The city is 230 km west of the border with Pakistan and 90 km north of the Sea of Oman.
Two police officers were killed in the second attack, which took place in Khash town in the same province.
No group or individual immediately took responsibility for the terrorist attacks.
In September, gunmen killed four border guards in the province in two separate attacks. The terrorist group Jaish al-Adl claimed responsibility for one the attacks, in which one officer and two soldiers in the border guard were killed.
The province, bordering Afghanistan and Pakistan, has been the site of occasional deadly clashes involving terrorist groups, drug smugglers and Iranian security forces.