The Islamic State group tapped into longstanding feelings of neglect and resentment by Sunnis toward the Shiite-led government in its advance. But the group risks losing some of its initial popular appeal as difficulties mount in governing the “caliphate” it declared across parts of Syria and Iraq, still home to as many as 8 million people.

Residents in Fallujah and Mosul report shortages of fruits, vegetables and cooking gas, causing significant price hikes. Power outages are frequent. The militants are growing distrustful, killing locals they believe have tipped off the U.S.-led coalition.

Abdul-Rahman Mushrif, a Fallujah grocery store owner, said two of his brothers fled the city at the height of the violence last year and have been unable to return for fear that they could be killed.

“They could not attend the funeral of our youngest brother and our father because the city is under siege,” he said. “Our situation is miserable. We lack almost everything.”