Tens of thousands of people live in the camps, which swelled enormously during the months-long battle that culminated in the defeat of the last vestige of the Islamic State group's "caliphate" by a Kurdish-led alliance.
"A delegation from the Iraqi cabinet visited the autonomous administration to discuss the return to Iraq of displaced Iraqis, estimated to number 31,000, and an agreement was reached," Kurdish official Mahmud Kero told AFP.
"So far 4,000 people have signed up and we are waiting for the Iraqi government to open up the Iraqi border to start," he said.
Kero said many of the displaced did not have Iraqi identity papers, including children born on Syrian soil.
"We have asked the Iraqi government to find a solution," he said.
Those expected to return do not include suspected IS fighters being held in Kurdish-run jails, after surrendering or being caught fleeing the jihadists' last stand.
"We have asked for the return of all Iraqis including those accused of belonging to IS," Kero said.
The Kurdish-led Syrian Democratic Forces announced the defeat of the IS "caliphate" last month after tens of thousands of people streamed out of the last patch of jihadist territory in the eastern village of Baghouz near the Iraqi border.
But the jihadists maintain a presence in Syria's vast Badia desert as well as sleeper cells in populated areas, and have continued to claim deadly attacks in areas controlled by the SDF.
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