Iraqi Kurdish forces backed by air power retook three villages from jihadist militants northeast of Baghdad on Monday and also held off two assaults elsewhere, officials said.

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, a peshmerga brigadier general said.

He added that Kurdish troops are close to sealing off all entrances to the town of Jalawla itself, which they have sought to recapture for weeks.

Farther 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.