DAHUK, Iraq—Of all the many ancient peoples who once lived in the land between the Tigris and the Euphrates, Iraq's Assyrian Christians pride themselves on having persisted in their traditional homeland for millennia, even as other civilizations thrived then disappeared, as languages and cultures died out, as ethnic groups melted into the ways and genetic pools of their conquerors.

But today Iraq's Assyrians, and its Christians in general, fear that their place in this multiethnic, multisectarian mosaic society is shrinking, under severe threat from the ultraconservative Islamist group the Islamic State (IS).

It isn't the first time that Iraq's Christians have faced such a foe. The IS's earlier incarnation, al Qaeda in Iraq—a group that formed after the U.S.-led invasion