Police officials said that the deadlier of the two attacks occurred on Saturday morning in a commercial street in the al-Ameen district, killing four people and wounding 18 others. Several shops were damaged in the attack.
Another police official said one policeman was killed and two others were wounded after a car bomb struck a police convoy in the northern city of Mosul.
Two medical officials confirmed the casualty figures.
Violence has spiked in Iraq in recent weeks, raising fears of a return to widespread sectarian bloodshed.
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