The move marks a shift in priorities for the US following the collapse of the extremists' so-called caliphate late past year.
The reported agreement comes three months ahead of Iraqi elections in which the presence of U.S. troops in the country is expected to be a divisive issue.
An AP reporter at the base saw troop movements matching the officials' account.
The statement came the same day as an Iraqi official claimed the United States would be reducing its presence in the country since the "battle against Daesh (IS) has ended".
The Iraqi spokesperson stressed the drawdown was still in its early stages and does not mark the beginning of a complete pullout of USA forces.
A coalition spokesman declined to confirm or deny that the drawdown had begun.
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"That's correct, but I can not talk numbers and specifics on the shift", Pahon said Monday when asked to confirm media reports that USA troops in Iraq will be moved to Afghanistan.
"The next stage will turn from military cooperation to training and arming the Iraqi forces", Hadithi said.
For example, the U.S. Air Force Central Command, launched a new training and advising team in Iraq last week.
The global anti-terrorist coalition, led by the United States, assisted Iraqi forces in recapturing territory seized by Daesh jihadists, including the liberation operation of the country's second-largest city Mosul.
The coalition statement revealed its troops would remain in Iraq as IS extremists "continue to pose a threat" to the country's security and risk transition back into an insurgency.
US Army 1st Lt William John Raymond based at Al-Asad told AP: "We're had a recent change of mission and soon we'll be supporting a different theater of operations in the coming month".
He spoke as he and a handful of soldiers from his unit conducted equipment inventory checks required before leaving Iraq.