Death tolls being reported ranged from 29 up to the mid-30s.
A car bomb killed 19 people when it exploded next to a bus of Shiite pilgrims returning from the annual Arbaeen festival in Karbala, the BBC said.
The Arbaeen holy day marks the end of a 40-day mourning period for Imam Hussein, the Prophet Muhammad's grandson, CNN reported. Hundreds of thousands of people attended the festival Saturday.
In another explosion, a suicide bomber killed 10 people on a minibus in eastern Baghdad, the BBC reported.
CNN reported that three guards were killed and three badly injured when a bomb exploded in the lobby of the headquarters of the Sunni Iraqi Islamic Party in southern Mosul Sunday afternoon.
Sunday's explosions came a day after a major international summit in Baghdad was convened to discuss security and sectarian violence in Iraq.