Prime Minister Haider al-Abadi told an international meeting in Paris that the four-day-old offensive was "advancing faster than expected".
France and Iraq were co-chairing the meeting on the future of Mosul, which observers have warned could raise even greater humanitarian and interconfessional challenges than the massive military operation to retake it.
In some areas, the Iraqi advance was met by a trickle of civilians fleeing both the fighting and the jihadists who ruled them for two years, but the feared mass exodus from Mosul had yet to materialise.
"The objectives are to clear a number of nearby villages and secure control of strategic areas to further restrict ISIL's movements," the peshmerga command said, using an alternative acronym for IS.
At around 6:00 am (0730 IST), bulldozers flattened a path for forces in armoured vehicles to carve their way down towards Bashiqa.
As tanks and personnel carriers prepared to advance, a shadow glided above them and one peshmerga shouted "drone!"
An AFP reporter in the village of Nawaran near Bashiqa saw the downed drone, a Raven RQ-11B model similar to a booby- trapped one that killed two Kurdish fighters and wounded two French soldiers a week ago.
"These drones belong to IS... So we shot this drone and brought it down. As you can see, the peshmerga destroyed it," said General Aziz Weysi, commander of the peshmerga's elite Zaravani task force.
Iranian Kurdish rebels of the Kurdistan Freedom Party (PAK) were involved in the operation alongside the peshmerga and apparently taking a frontline role.
East of Mosul, where the peshmerga launched the offensive on Monday, Iraq's elite federal counter-terrorism service was taking control of Bartalla, a town whose mostly Christian residents fled the IS advance two years ago.
"There is resistance, we already blew up three car bombs today," Lieutenant General Abdelwahab al-Saadi, who is commanding operations in the area, told AFP by telephone.
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