Iraqi federal and paramilitary forces on Sunday said they lost five men in last week's clashes with Kurdish fighters, bringing the death toll for all sides to 31.
On Friday, Iraq's central government said its forces had taken back control from the Kurds of all disputed territory in the north of the country located outside the Kurdish autonomous region.
The areas were captured as part of a sweeping operation by federal forces after a controversial Kurdish independence vote.
A statement by Iraq's Joint Operations Command said two federal forces were killed in Altun Kupri region of Kirkuk province, which was taken on Friday.
A spokesman for the Iranian-backed Hashed al-Shaabi paramilitary force told AFP the militia lost three of its fighters in the clashes with the Kurds.
Peshmerga commander Wasta Rassoul had on Friday said 26 Kurdish fighters were killed and 67 others wounded in last week's clashes.