Iraqi officials say scattered violence across the country has killed at least 19 people.
Bomb attacks in Tal Afar 420 kilometers northwest of Baghdad and Baghdad targeted Iraqi security forces.
Several more bodies showing signs of torture were also found in the Iraqi capital.
A Sunni militant group said Sunday that it recently executed 10 Shi'ites from India and Pakistan.
It is unclear if the victims were among 14 South Asian Shi'ite pilgrims killed earlier this month.
The U.S. military has forecast an increase in attacks during the Muslim holy month of Ramadan, which began for Iraq's Sunnis on Saturday, and is due to start for Iraqi Shi'ites on Monday.
Prime Minister Nouri-al-Maliki urged Iraqis to put aside their differences during the Muslim holy month following Saturday's bomb attack that killed more than 30 people in a Shi'ite area of Baghdad.
Information for this report is provided by AP, AFP and REUTERS.