Fighting between the Islamic State of Iraq and the Levant (ISIL) and Sunni militias is raging in the west of Iraq's Anbar province, with a fierce battle taking place for control of the strategic town of Heet.

ISIL had reportedly seized control of most of the town on Thursday, but Sunni militias, fighting on behalf of Iraq's government, swiftly denied the claim saying the battle was ongoing.

State television said the armed group had occupied the mayor's office and police station but were locked in fighting with the local Sunni Albu Nimr tribe.

Al Jazeera's Imran Khan, reporting from the capital Baghdad, said the town had yet to fall - with ISIL fighters unable to move in and out freely.

"ISIL does control huge chunks of Anbar province... but we're seeing a renewed push by the Iraqi army and those Sunni militia groups," he said.

Khan added that the fighting appeared to have sparked again over the past three days, prompted by US and French air strikes on an ISIL base-camp last week.

"That seems to have weakened them significantly, allowing these ground troops to go in and try and start clearing areas within Anbar province," Khan said.

Heet is a walled market town 30km from Anbar's provincial capital Ramadi, and lies close to the Ain al-Asad military base, one of Iraq's largest defense facilities.

Anbar Province, which borders Syria, has been a major stronghold for ISIL and continues to be largely controlled by the group.

ISIL have captured vast swathes of western and northern Iraq including the north's biggest city Mosul, as well as large areas of the east and north of neighbouring Syria.