Baghdad - The Islamic State of Iraq and the Levant has said it has taken more territory in Anbar province even as Iraq's army and pro-government Sunni fighters continue to go after the armed group.

Iraq's government forces are currently in the town of Ameriyah in Fallujah. This is a strategic town that links Anbar to Baghdad and the south of the country. By holding Ameriyah against the ISIL fighters, the army can ensure that supplies from the capital reach Anbar.

There are only a few kilometres between the ISIL fighters and the troops as ISIL keeps up the push towards the city, despite an expanding US-led campaign of air attacks.

"We will never leave our city," Major Aref Mohammed al-Janabi told Al Jazeera. "This is our homeland that we cannot abandon just because there is a conspiracy on this country - we will fight them whether they call themselves rebels, or armed groups."

But casualties remain a key concern for the army, which relies on shelling and tank fire.

On Sunday, witnesses told the AP news agency that they saw ISIL fighters publicly kill six Iraqi soldiers in Anbar province.

The agency said that the soldiers, one in uniform and five in civilian clothes, were lined up against a wall in the town of Hit and shot in the head.

They said the ISIL fighters also bombed a police station in Hit, which was stormed on Thursday.

On Sunday, the US military released a statement saying that it had conducted four air raids northeast of Fallujah and one southeast of Hit.

Follow Imran Khan on Twitter at @AJImran

Source: Al Jazeera