A car bomb in a bus station in the city of Karbala, southwest of Baghdad, killed at least 37 people and wounded more than 40. Police said they feared the death toll would rise.
Reports said the bomb went off near the Imam Hussein shrine, one of the most important holy sites for Shi'ite Muslims.
In Baghdad, a suicide attacker blew up his vehicle packed with explosives at a checkpoint on a bridge over the Tigris River.
It was the second attack on a Baghdad bridge this week.
Police said at least eight people were killed and more than a dozen wounded.
On April 12, a truck bomb killed at least seven people on a bridge in northern Baghdad, heavily damaging the structure.
(compiled from agency reports)