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"Your security forces are now coming to liberate you," said leaflets dropped by the Iraqi air force on the western border region of al-Qaim and Rawa, according to a statement from the Joint Operations Command in Baghdad.
The militant group also holds parts of the Syrian side of the border, but the area under their control is shrinking as they retreat in the face of two sets of hostile forces - a U.S.-backed, Kurdish-led coalition and Syrian government troops with foreign Shi'ite militias backed by Iran and Russia.
Islamic State's self-declared cross-border caliphate effectively collapsed in July, when U.S.-backed Iraqi forces captured Mosul, the group's de facto capital in Iraq, in a gruelling battle which lasted nine months.
The militants' Syrian stronghold, Raqqa, fell to U.S.-backed forces last week.
Islamic State leader Abu Bakr al-Baghdadi, who declared the caliphate from Mosul in mid-2014, released an audio recording on Sept. 28 that indicated he was alive, after several reports he had been killed. He urged his followers to keep up the fight despite setbacks.
"God is with us in this last assault on Daesh members," said the leaflets dropped by the Iraqi forces on the border area with Syria, referring to Islamic State.
"Tell those among your children and relatives who took up a weapon against the state to throw it aside immediately, and to go to any house on top of which a white flag have been raised when the liberation forces enter al-Qaim."