Among the goals is the Sinjar area, which was home to many members of the Yazidi minority before IS jihadists attacked in early August and forced most of them to flee.
The risk of a genocide against the Yazidis was one of the reasons US President Barack Obama put forward for launching a campaign of air strikes against the IS group.
The two-pronged push was launched from Rabia, on the border with Syria, and Zumar, on the shores of Mosul dam lake, said senior officers in the Kurdish army known as the peshmerga.
"The attack is ongoing and has the support of coalition jets which have been targeting IS positions in Zumar and Sinjar (regions) since last night," he told AFP.
The peshmerga had already recaptured three small villages, the officer added.
The chief of staff of Massud Barzani, the president of Iraq's autonomous Kurdish region, said the aim was to reclaim the entire Sinjar area.
"The plan to liberate Sinjar was reviewed by the Kurdish leader and the peshmerga field commanders. God willing, we will liberate it soon," Fuad Hussein said.
The 60-kilometre-long (40 miles) range was the scene in August of one of the most dramatic episodes of the assault on Iraq the jihadists launched in early June.
IS fighters killed hundreds of residents, abducted and enslaved hundreds of Yazidi women and girls and forced tens of thousands of people to seek refuge on Mount Sinjar.
Civilians remained besieged for days in the searing summer heat with little to eat and drink.
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