Militants led by the Islamic State (IS) group overran large chunks of Iraq in a lightning June offensive that swept security forces aside.

But Iraqi federal forces and the autonomous Kurdish region's peshmerga fighters are now fighting to regain ground from the militants on multiple fronts.

On Monday, Kurdish forces backed by Iraqi air support retook three villages in the Jalawla area in Diyala province, as well as a main road used by jihadists to transport fighters and supplies, peshmerga members said.

"Jalawla is strategic because it is a gateway to Baghdad," Shirko Merwais, a senior Kurdish political party official in nearby Khanaqin, told AFP.

In the area, Iraqi aircraft are "carrying out air strikes and the peshmerga... are fighting on the ground," he said, adding that "in the beginning, coordination between the peshmerga and the Iraqi government was poor, but now, after the danger posed by (IS) grew, it has become much better".

Further north, militants launched two assaults on the Shiite Turkmen-majority town of Tuz Khurmatu, late on Sunday and early Monday.

Both attacks were beaten back by Kurdish forces supported by Iraqi aircraft, officials said.

On August 8, the United States launched a campaign of air strikes against militants who were pushing back Kurdish troops and threatening Arbil, the capital of their northern region.

Dozens of strikes have helped the Kurds regain ground, including an area called Qaraj, which they retook on Sunday.

Despite calls from the government in Baghdad and other forces battling militants in the country, Washington has yet to expand the campaign outside northern Iraq.

However, the United States has said that air operations against the jihadists in Syria may also be necessary.

strs/wd/pdh