ERBIL, Iraq—Islamist militants took over Mosul so easily that a mother of four and her family slept right through it. By the time they woke up on Tuesday morning, masked men were patrolling the streets with machine guns drawn.

It was a scene that could have been ripped from the pages of a thriller novel. But the masked, gun-toting commandos didn't frighten her nearly as much as the savage counterattack she expected from Iraq's security forces, she said.

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