The statement did not disclose if the realignment of US personnel might lead to a future troop reduction though an Iraqi official told The Associated Press that USA troop levels could be reduced by 60 percent.
The U.S. ambassador Douglas Silliman had told local media "the presence of U.S. forces in Iraq has been decreased, especially in Anbar province in coordination with the Iraqi forces".
Daesh has been driven out by the Iraqi army, backed by a US -led coalition, from territory overran by the terrorist group in northern and western Iraq in 2014.
There were roughly 9,000 USA troops in Iraq last September, according to a Pentagon report.
The contractors say dozens of American soldiers have left on daily flights over the past week.
An AP reporter at the Al-Asad base in western saw troop movements reflecting the contractors' account.
Two Iraqi officials confirmed that USA -led coalition and Iraqi government have reached an agreement to draw down troops in Iraq.
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That would leave some 4,000 USA troops to continue training the Iraqi military.
The U.S. first launched airstrikes against the Islamic State group in in August 2014.
Despite that information, the US military cites the official number of USA troops in Iraq as approximately 5,262. Iraq's oil ministry has ordered the state-held North Oil Company to draft "an urgent plan" for rehabilitating the oil fields in Nineveh.
Iraq declared victory over Daesh in December after more than three years of grueling combat against the extremists in a war Iraqi forces fought with close USA support.
The move comes just weeks after Defense Secretary Jim Mattis announced the United States' new defense strategy. In 2014, at the height of the Sunni militant group's power, IS controlled almost a third of Iraqi territory.
"The Coalition will tailor our forces in consultation with our Iraqi partners in order to ensure the lasting defeat of Daesh", said Brig.
"We've had a recent change of mission and soon we'll be supporting a different theater of operations in the coming month", U.S. Army 1st Lt. William Raymond told the Associated Press.
Hashemi added that part of the U.S. troops would be sent to Afghanistan.