Fanning fears of leaders in Baghdad, Christians are pressing for their own semiautonomous region in northern Iraq, much like the one the larger Kurdish minority group already has. The Yazidis already have an active militia that has been battling Islamic State militants for months.

“There is a fear of dividing the country due to demands made by different groups in Iraq,” said Ghassan al-Husseini, an adviser to Prime Minister Haider al-Abadi. “We believe that all minorities have the right to defend themselves, especially in their own areas. But we also believe it should not be away from the government.”

Mr. Abadi and other officials acknowledge that given the Iraqi military’s advanced state of disrepair, small ethnic and religious groups should be allowed to fight back and, in some cases, with close government supervision, receive arms and training from the state.

But the same officials worry that these calls to arms will lead to calls for autonomy and may end up wresting political authority from Baghdad in a country already on the brink of splitting apart.