“There is now a public acceptance of the idea of separation, and this acceptance stems from the facts on the ground,” said Zuheir al-Sharba, deputy secretary-general of the Imam Ali Shrine in Najaf, one of Shiite Islam’s main pilgrimage centers. “The facts on the ground are clear. Before 2003, I as an Arab from Najaf could go to Erbil and buy a house and live there. It is no longer permitted to me. And now it is also not possible for me in Mosul, either.”

Openly sectarian policies by former Prime Minister Nouri al-Maliki, who ruled in 2006-2014, have contributed to this split, and to the rise of Islamic State, by alienating many Sunni Arabs and Kurds. The new prime minister, Mr. Abadi, has adopted a more embracing tone, promising national reconciliation and a more inclusive government. He struck a deal on sharing oil revenues with the Kurds and appointed a Sunni as minister of defense. His outreach, however, may be too little too late.

“Iraq is passing through a final stage now. Either it will rectify itself or, God forbid, it will be facing a huge catastrophe,” Iraqi Vice President Ayad Allawi, a nonsectarian politician and former prime minister, said in an interview “This is the last mile for Iraq.”