The peshmerga began their assault early on Tuesday in the village of Basheer, which IS captured in June and has used as a base for operations against Kirkuk, a key oil town 15km to the north.
A senior peshmerga source told the AFP news agency that his forces, backed by US-led coalition jets, also attacked the town of Zumar, near the reservoir Mosul dam, Iraq's largest.
They also went on the offensive north of the IS-controlled city Mosul, Iraq's second largest.
Al Jazeera's Monica Villamizar, reporting from Erbil in northern Iraq, said the Kurds had been boosted by air attacks on IS by the US-led coalition.
"Peshmerga fighters have been in stalemate with the ISIL in the past, but now this is changing. At least in two of these attacks, air strikes were also involved," our correspondent said.
She said the strikes had emboldened peshmerga, who could previously not match the firepower of IS.
Halgord Hekmat, of the peshmerga, told AFP: "We have pushed IS from 30 positions, including in the Zumar and Rabia areas."
He said the advances would aid efforts to retake Sinjar, a town further southwest which IS captured in early August, prompting tens of thousands of civilians, mostly from the Yazidi minority, to flee.