The coordinated attacks took place in Shiite neighborhoods.
The Islamic State of Iraq claims the assaults were meant to support Sunnis in prisons and in memory of those who were executed.
Meantime, there was another attack in Baghdad on Monday at a police checkpoint.
Officials said a suicide bomber set off a car bomb, killing seven and wounding dozens.
Those were the first two attacks in Iraq since U.S. troops withdrew from the country earlier this month.
U.S. and some Iraqi officials have warned of a resurgence of Sunni and Shiite militants and an increase in violence after the U.S. troop withdrawal.
Along with the security challenge, Iraq is facing an increase in political tension as Iraq's Shiite prime minister, Nouri al-Maliki, is engaged in a showdown with the top Sunni political leader in the country.
The Associated Press contributed to this report.