The Iranian-backed Shiite militia groups in Iraq that helped take control over Kirkuk and the surrounding oil-rich region from the Kurds have begun to eye the capital of Baghdad, where they plan to press for changes that could strain a tenuous peace in the region following the fall of ISIS.

Kirkuk became a flashpoint for the Iraqi government after the Kurdistan Regional Government’s (KRG) Sept. 25 referendum on independence, which passed. Some believe the vote was an attempt by KRG President Masoud Barzani to strengthen his political position in Iraqi Kurdistan.

But over the past few years the Popular Mobilization Forces (PMF), an umbrella organization under while many of the Shiite militias fall, has emerged as a powerful political force in Iraq. Coming off successful campaigns against the nearly-defunct Islamic State, the group has been empowered (by Iran) to press its political advantages.

The group wants Baghdad to remain steadfastly opposed to any Kurdish independence — a position held by Iraq but also Iran, Syria and Turkey, each of which has a Kurdish population. Also, the PMF wants Baghdad to curtail its alliance with the United States. These are viewed as uncompromising positions:

Having crushed the Islamic State in much of Iraq and recaptured Kirkuk, Iraq’s Iran-backed militias are now oozing with confidence. They are determined to hold on to the power that their members have fought and died to acquire, and they wish to be seen as a legitimate force — not an unorganized, unkempt bunch of fanatics.

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