Three soldiers were killed and five injured when unknown gunmen attacked a security checkpoint in al-Dulaya, 170km north of Baghdad.
One civilian was killed and seven wounded in a bomb blast in Baquba, 60km north-east of Baghdad, police said.
No group has claimed responsibility for the attacks.
Iraq has seen a recent surge in violence targeting Shiite Muslims and security forces, as tensions between the Shi'ite-led government and the Sunni minority widen.
Sunnis have for two months been calling on Prime Minister Nouri al-Maliki, who is a Shi'ite, to repeal laws they say are used to target them.