At one house, Iraq’s national flag fluttered atop a building that Iraqi soldiers had captured from militants two days before. At another, smashed household goods and furniture were scattered on the floor. Outside a third, hosting a meeting of Iraqi security force commanders, a captain from Iraq’s national intelligence service pointed to the far side of a murky irrigation canal. “Here it is safe now,” he said of Al-Daira. “But over there are more terrorists. That is where we will fight...