Asked about the referendum, White House spokeswoman Sarah Sanders said on Monday: "We hope for a unified Iraq to annihilate ISIS and certainly a unified Iraq to push back on Iran."
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The U.S. State Department warned the Kurds last week that "holding the referendum in disputed areas is particularly provocative and destabilizing."
The referendum was held not only in the Kurdish autonomous region of Iraq, but also in areas in the north of the country where Kurdish forces have advanced against Islamic State. These areas also have large non-Kurdish populations.
Turkey said it did not recognize the referendum and would view its outcome as null and void, adding that the Iraqi Kurdish government was threatening the peace and stability of Iraq and the whole region.
Prime Minister Binali Yildirim said his government was evaluating possible punitive steps regarding its border with northern Iraq and air space in response to the vote.
Erdogan said traffic was only being allowed to cross from the Turkish side of the border into Kurdish areas of Iraq.
Ankara's forces are again fighting a Kurdish insurgency in Turkey following the collapse of a peace process.