Iraqi forces are conducting operations to set the stage for an assault on Mosul, the country's second city that has been held by IS since June 2014, but the final push to retake it is likely still months away.
"A number of the families... and leaders of (IS) in Mosul, they and their families sold their belongings and withdrew towards Syria," whose border west of the city, Obeidi told Iraqiya state television.
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Some also sought to infiltrate towards Iraq's autonomous Kurdish region, located north and east of Mosul, Obeidi said during an interview which was broadcast on Saturday night.
Mosul is the last city held by IS in Iraq, but retaking it poses a major challenge, and the operation could unleash a humanitarian crisis unless plans are made for people who would likely flee the fighting.
The Red Cross has said it believes that up to a million Iraqis could be displaced in the coming months by fighting against IS, including the operation to recapture Mosul.
IS overran large areas north and west of Baghdad in 2014, but has since lost significant ground to Iraqi forces backed by US-led air strikes, training and other assistance.