Middle East

Battle for Iraq's Fallujah continues

US-backed Iraqi forces fighting IS militants in Fallujah are advancing towards jihadist strongholds. (AAP)

The battle to recapture Fallujah from Islamic State militants has entered its fifth week, with half of the Iraqi city yet to be retaken.

US-backed Iraqi forces fighting Islamic State militants in Fallujah are advancing towards jihadist strongholds in western districts where they expect the final push to recapture the city will take place, the Iraqi commander says.

Prime Minister Haider al-Abadi declared victory on Friday after troops reached the centre of the city, an hour's drive west of Baghdad, but an official in the US-led coalition said on Sunday Iraqi forces had so far taken only half of Fallujah.

The operation to recapture the Iraqi city longest held by Islamic State entered its fifth week on Monday, and fighting has forced more than 85,000 residents to flee to overwhelmed government-run camps.

Iraqi forces continue to face shooting, suicide bombs and mortar attacks as they confront militants north of a road running through the city.

Heavily armoured Interior Ministry police units were pressing towards Golan neighbourhood, on the northwestern edge of the city, Lieutenant General Abdul Wahab al-Saidi told Reuters on Monday at his temporary command post in a southern district.

"The biggest effort now is on the western axis. If they collapse on the western axis and our forces reach Golan, you won't hear any more shots inside Fallujah," he said.

Troops from Saidi's counter-terrorism force were fighting Islamic State in al-Dhubat district, further east.

Fifty militants were killed there by coalition air strikes on Sunday and at least 15 others died in clashes, the commander said.

Army troops moving north from the neighbourhood of Shurta had not yet entered al-Jughaifi area on the city's northern edge, while units from Baghdad operations command were advancing in the easternmost district of Askari, according to Saidi.

Sitting with other officers from the elite counter-terrorism service at a plastic picnic table littered with walkie-talkies inside an unfinished building, Saidi said the battle would end soon.

Most of the militants, including a few hundred foreign fighters, were killed or captured trying to escape with civilians, he said. Only six counter-terrorism commandos had been killed.

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