The assault, launched early Sunday northeast of Baghdad in Diyala province, is the latest in a series of drives that have seen some territory lost to a sweeping June offensive by the Islamic State group being regained.
"Army and police and (militia) forces attacked from the southern and western sides of the Jalawla and Saadiyah (areas), while (Kurdish) peshmerga forces attacked from the northern and eastern sides of Saadiyah," Staff General Abdulamir al-Zaidi told AFP.
Accounts differed as to the extent of the gains in the two areas, with some sources saying they had been retaken and others reporting parts were still outside government control.
"The number of peshmerga killed is 20 and more than 40 were wounded during clashes against (IS) and by bombs at the entrance of Jalawla, inside Jalawla and in Saadiyah," peshmerga commander Mahmud Singawi told AFP.
Karim al-Nuri, a senior commander in the Badr militia, which took part in the operation, had earlier said bombs killed 12 members of the anti-IS forces.
He did not specify whether those killed were from the government security forces, Shiite militiamen, tribesmen or Kurdish fighters.
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Explosive devices hidden beside or under roads and planted in buildings are a hallmark of IS, taking a toll on its enemies even after it withdraws or is forced out of an area.
An army brigadier general said Saadiyah and Jalawla were "the main centres of support for (IS) militants", whom security forces are seeking to isolate in the nearby Hamreen mountains.
The two areas are also important because of their proximity to the autonomous Kurdish region, which is battling the jihadists, and to the border with neighbouring Iran, which is also helping Iraqi forces.
Sunday's operation came on the heels of another that saw the strategic northern town of Baiji retaken from the militants and a months-long siege of Iraq's largest oil refinery broken.
Security forces and pro-government fighters also retook the Jurf al-Sakhr area south of Baghdad, which had posed a threat to both the capital and the Shiite shrine city of Karbala, which millions of pilgrims visit each year.
However, the militants sill hold large areas of the country, including the key cities of Mosul, Tikrit and Fallujah.
IS spearheaded a major offensive in June that overran much of Iraq's Sunni Arab heartland, sweeping security forces aside.
Backed by a US-led campaign of air strikes and by international advisers, Shiite militiamen and Sunni tribesmen, they are now performing better, but still face major challenges in the battle against IS.