A mass grave containing the remains of around 400 people has been found near the Islamic State-controlled city of Fallujah, where government forces are pressing on with an offensive to retake it from the extremist militia, military sources say.

Iraqi forces uncovered the grave in Fallujah's north-western suburb of Saqalawiya on Sunday, a day after the government said it had recaptured the largely agricultural area from Islamic State.

"Most of the remains belonged to military personnel who were detained and killed by the organisation," said one military official on condition of anonymity, referring to Islamic State.

There was no official confirmation in Baghdad.

Saqalawiya and Fallujah were among the first areas seized by Islamic State in western Iraq in early 2014.

Six months later, the radical Sunni group stormed through Sunni areas of northern Iraq, taking the country's second-largest city, Mosul.

Two weeks ago, government troops, backed by allied Shi'ite militiamen and a US-led air alliance, started an onslaught to retake Fallujah, around 50 kilometres west of the capital Baghdad.

The forces on Sunday drove Islamic State fighters from several southern suburbs of Fallujah, boosting their advance on the city, Yasser Khalaf, an army commander, said.

The US-led coalition also carried out a series of airstrikes against militant targets in the area, he told dpa without giving details.

In recent months, Islamic State has suffered major military setbacks in Iraq and neighbouring Syria.