The IS assault on areas south and west of the northern city of Kirkuk began at around midnight, sparking fighting with medium and heavy weapons that was still ongoing today morning, a police brigadier general said.
Brigadier General Shirko Rauf and five other members of the Kurdish peshmerga forces were killed in clashes, while 46 more were wounded, the police officer and a doctor said.
The Kirkuk province security committee announced a curfew beginning at 10:00 am (1230 IST) today, saying it will be in effect until further notice.
Several Iraqi divisions collapsed in the early days of the offensive, clearing the way for the Kurds to take control of a swathe of disputed northern territory that they have long wanted to incorporate into their region over Baghdad's objections.
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But after driving south towards Baghdad, IS turned its attention to the Kurds, pushing them back towards their regional capital Arbil in a move that helped spark US strikes against the jihadists.
The conflict is redrawing some of the de facto internal boundaries of Iraq in favour of broader Kurdish control in the north.