The attacks appeared to be coordinated and targeted police and Shiite pilgrims. The Iraqi wing of al Qaeda said it was behind at least one of the attacks near Baghdad's heavily guarded Green Zone.
Officials said two car bombs exploded in a crowded shopping and restaurant area in Karbala, killing 13 people there. Similar attacks were reported in Kirkuk and Baghdad.
Authorities have been bracing for attacks in the run-up to the Arab League summit. The violence comes on the ninth anniversary of the U.S.-led invasion to bring down Saddam Hussein. To mark the anniversary, a protest was scheduled for 5 p.m. outside the federal building in Los Angeles.
The Associated Press contributed to this report.