Shelling struck a street in the Tunis area of northern Baghdad where Shiites were distributing refreshments from a tent on Monday, after which a suicide bomber detonated explosives in the same area, a police colonel said.
The attacks killed at least 11 people, while shelling in the Shiite-majority Kadhimiyah area, also in north Baghdad, left at least five people dead.
The Islamic State jihadist group, which considers Shiites to be heretics and has overrun large areas of Iraq, said in an online statement that a suicide bomber identified as Abu Khattab al-Iraqi carried out the attack in Tunis and a rocket attack in Kadhimiyah.
The statement did not mention shelling in the Tunis area, but appeared to be referring to the same incidents.
IS also claimed two car bombs targeting Shiites on Sunday that killed at least 18.
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Iraq has implemented heavy security measures involving tens of thousands of security forces members and allied militiamen to protect Shiites during the Ashura religious commemorations.
Hundreds of thousands of Shiites flocked to the shrine city of Karbala south of Baghdad for Ashura, which marks the death of Imam Hussein, one of the most revered figures in Shiite Islam.
Ashura processions were also held in Baghdad and other parts of the country.
Shiites have been targeted during Ashura before, but this year's commemorations face even greater danger with IS in control of large areas of Iraq.
But as of early evening, there were no reported attacks during the peak of the commemorations on Tuesday.