Five people died when a car bomb tore through a market in Kut city, some 160 km from Baghdad. About 70 others were wounded, Xinhua reported.
The second attack took place in Meshahda, 30 km from the capital. Gunmen went on a shooting rampage near a check point, killing 10 soldiers and wounding 10 others.
Earlier in the day, at least 29 more were killed in a series of bombings and shootings in the country.
Thursday’s deadly attacks come as Iraqis marked the end of the Islamic holy month of Ramadan.