AMRIYAT AL FALLUJAH, Iraq—Food is in short supply and the water is always too hot to drink in this sun-baked desert camp for thousands of Iraqis who have fled the Islamic State-held city of Fallujah.

But most of the uprooted Iraqis here, all of them Sunni Muslims, had only one complaint for visiting government officials this week: Where are our men? The question was shouted often, sometimes through tears, by desperate women searching for their husbands, brothers and fathers.

...