Iraqi troops, including Shiite Muslim militias incorporated into Iraq’s armed forces, are already in the area, and the American-led coalition is battling Islamic State militants elsewhere in the Kirkuk region. Kurdish troops known as pesh merga are deployed in the multiethnic city of Kirkuk, which they seized when the Iraqi Army fled an assault by the militants in 2014.

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Chris Mcgrath/Getty Images
The inclusion of Kirkuk and other disputed areas in the referendum enraged the Iraqi…