The helicopter was shot down during a large-scale operation against militants in a desert area west of Baiji, north of Baghdad, killing two crew members and two soldiers who were on board, army officers said.
Helicopters are periodically hit by gunfire during operations, including one last month in which a pilot was wounded.
In the northern city of Kirkuk, a car bomb detonated near the governorate headquarters, killing two people and wounding 15.
In Nineveh province, also in the north, attacks killed three people, and soldiers shot one militant dead. Violence in Diyala province left two people dead and two wounded.
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Violence has reached a level unseen since 2008, and there are fears Iraq is slipping back toward the intense Sunni-Shiite bloodshed that peaked in 2006-2007 and killed tens of thousands.
Iraq saw a sharp spike in violence including a series of bloody sectarian attacks in September, with the UN putting the monthly death toll at almost 1,000.