Elite forces reinforced positions that were taken since a fresh push south of Mosul was launched on Sunday while hundreds of civilians fled newly recaptured villages.
"Around 480 people displaced from Al-Yarmuk area are being transferred to liberated areas further south," the federal police said in a statement.
Iraqi forces have retaken a key checkpoint on the main Baghdad highway south of Mosul and the village of Al-Buseif, a natural citadel overlooking the airport and the south of the city.
However Hashed al-Shaabi (Popular Mobilisation) paramilitaries continued to battle jihadists further west, near the town of Tal Afar, which lies between Mosul and the Syrian border and is still held by IS.
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The Hashed al-Shaabi said in a statement they blew up at least four car bombs in fighting near Ain al-Tallawi and killed several IS members.
The elite Counter-Terrorism Service (CTS) that retook east Mosul and did most of the fighting since the offensive on the city was launched on October 17 have not yet been brought into action in the latest push.
Senior US officials this week estimated there were only 2,000 IS fighters defending west Mosul, suggesting the jihadist group had suffered heavy losses in the first four months of the operation.
The US-led coalition, which has provided intensive air support as well as advisers on the ground, said before the Mosul offensive began that 5,000 to 7,000 jihadists were in the city.
The fate of an estimated 750,000 civilians trapped in west Mosul was a major source of concern as Iraqi forces prepared for what many have predicted could be one of the bloodiest battles yet in the war on IS.
Almost half of the remaining population are children, according to aid groups, and supplies are fast dwindling.
"Daesh fighters have seized all the hospitals and only they can get treated now," an employee at the Al-Jamhuri hospital in west Mosul told AFP by phone, using an Arabic acronym for IS.