A senior US defence official later clarified that the situation was still fluid and plans could change.
"All US forces that withdrew from Syria received approval to enter the Kurdistan Region so that they may be transported outside Iraq. There is no permission granted for these forces to stay inside Iraq," the Iraqi military said in a statement.
It is unclear whether the US troops will use Iraq as a base to launch ground raids into Syria and carry out air strikes against Islamic State militants.
The additional US troops would add to the more than 5,000 American troops already based in the country, training Iraqi forces and helping to ensure that Islamic State militants do not make a comeback.
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