Iraqi officials have acknowledged desertions but described the numbers as insignificant.
However, the desertions cast new doubt on the effectiveness of US-trained Iraqi security forces. The White House has conditioned further US troop withdrawals on the readiness of the Iraqi military and police.
Despite a drop in fighting, officials have insisted that the crackdown will continue until it breaks the stronghold by armed groups.
It was unclear, however, whether the freeze order might affect the plan.
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