Backed by warplanes from the US-led coalition, the fourth operation of its kind in the Kirkuk area left at least 10 Kurdish peshmerga forces and dozens of IS fighters dead.
"The offensive, launched from three fronts west of Kirkuk, included approximately 3,500 peshmerga," the Kurdistan Region Security Council (KRSC) said in a statement.
It said the offensive, which began at dawn, had cleared an area of 140 square kilometres (56 square miles).
The KRSC said coalition air strikes targeted 30 IS positions during the offensive, which peshmerga commanders said had achieved its goals.
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A peshmerga major general said 10 Kurdish troops were killed during the operation and at least 15 wounded.
"We lost those peshmerga because of IEDs," or improvised explosive devices the IS usually plants to slow enemy progress, he told AFP, speaking on condition of anonymity.
"We did not lose anybody in clashes because Daesh (an Arab acronym for IS) was running away from us as we advanced," he said.
Jaafar Sheikh Mustafa, the commander of peshmerga forces in Kirkuk, said 12 villages were retaken during the operation.
Several coalition air raids took place in the area in the hours leading to the offensive to pave the way for the ground assault.
In its daily breakdown of coalition air strikes on Iraq and Syria, the US military said eight strikes were carried out in the Hawija area and three near Kirkuk.