Syria's Kurds on Thursday announced a deal with Baghdad for 31,000 displaced Iraqis, mostly women and children, in camps in northeastern Syria to return home to Iraq.
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 ISIS'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 said.
"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.
Mr 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.
An Iraqi official said on Tuesday that Baghdad was making preparations for the return of tens of thousands of citizens, most of them "women and children".
Those expected to return do not include suspected ISIS fighters being held in Kurdish-run jails, after surrendering or being caught fleeing the insurgents' last stand.
"We have asked for the return of all Iraqis including those accused of belonging to ISIS," Mr Kero said.
The Kurdish-led Syrian Democratic Forces announced the defeat of the ISIS "caliphate" last month after tens of thousands of people streamed out of the last patch of ISIS territory in the eastern village of Baghouz near the Iraqi border.
But the extremists 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.
ISIS swept across a swathe of Syria and Iraq larger than Britain in 2014, declaring a "caliphate" in territory they held, but have since lost all of it to multiple offensives.