Kirkuk, inhabited by Kurds, Arabs and Turkmens, has long been the center of dispute between Baghdad and Kurdistan. A referendum on the city’s fate, originally scheduled for 2007 and a key component of the Iraqi Constitution the Americans helped write, has never been held.

But in 2014, as the Islamic State’s fighters bore down on the city and Iraqi soldiers dropped their weapons and ran, the Kurds took the city, which they consider a spiritual homeland and whose vast oil wealth could sustain an independent state.

The governor of Kirkuk, Najmaldin Karim, dismisses the argument that the Kurds have too many problems – an economic crisis, political divisions, the uncertain status of Kirkuk and other disputed areas – to seek independence now.

“Did the U.S. have a constitution when it declared independence?” he said. “No. Before African countries declared independence did they have everything in order?”

At 67, Mr. Karim is among a generation of Kurdish leaders who have come up in the Kurdish nationalist movement and now see, at the end of their careers, a chance to fulfill a long-held dream of independence. As a child, he saved his allowance to send money to the pesh merga, the Kurdish fighters who were battling the Iraq government then led by the Baath Party, to buy shoes and shirts.