FALLUJAH, Iraq (AFP) - Fighting erupted in Iraq's Fallujah on Wednesday after an Al-Qaeda-linked group urged fighters in the mainly Sunni Arab city to keep up their armed resistance against the Shiite-led government.

Fallujah and parts of the Anbar provincial capital Ramadi farther west have been outside government control for days - the first time militants have exercised such open control in major cities since the height of the insurgency that followed the 2003 US-led invasion.

Clashes broke out in two areas of Fallujah - Al-Askari in the east and Al-Shuhada in the west - and lasted for about an hour, witnesses said.

Both neighbourhoods were also shelled, they added.

It was not immediately clear who was involved in the fighting.

The Al-Qaeda-linked Islamic State of Iraq and the Levant (ISIL) has been active in the city but so have anti-government tribes.

The security forces have meanwhile recruited their own tribal allies in the fighting that has raged in Anbar province for more than a week and killed more than 250 people.

Near the provincial capital, soldiers backed by helicopters battled gunmen in the Khaldiyah area, a police captain said.

The fighting came after the release late Tuesday of an audio recording purportedly from ISIL spokesman Abu Mohammed al-Adnani exhorting Sunnis to continue fighting the Shiite-led government.

"Oh Sunni people, you were forced to take up the weapon," Adnani said.

"Do not lay the weapon down, because if you put it down this time, the (Shiites) will enslave you and you will not rise again," he said.

Defence ministry spokesman Staff Lieutenant General Mohammed al-Askari said Tuesday that soldiers deployed near Fallujah would hold off on a planned assault on the city for now.

"It is not possible to assault now" for fear of civilian casualties, Askari said.

Attacking the Sunni-majority city would also be extremely sensitive politically, as it would inflame already high tensions between the Sunni Arab minority and the government.

And it would be a major test for Iraqi security forces, which have yet to undertake such a major operation without the backing of US troops, who withdrew in December 2011.

Iraqi officials have said ISIL militants are holding Fallujah, and witnesses have seen the group's fighters in the city.

Prime Minister Nuri al-Maliki has called on Fallujah residents and tribes to expel ISIL to stave off a military offensive.

But some tribal leaders say the city is in the hands of armed tribesmen.

Tribesmen "are fighting to protect Fallujah and Garma (to its east) against army attacks," Sheikh Rafa al-Jumaili said on Wednesday.

Both Ramadi and Fallujah were insurgent strongholds in the years after 2003, and Fallujah was the target of two major assaults in which US forces saw some of their heaviest fighting since the Vietnam War.

They eventually wrested back control of Anbar with the support of Sunni tribesmen who formed the Sahwa (Awakening) militias, which allied with US troops against Al-Qaeda from late 2006.

But two years after US forces withdrew from Iraq, Sunni militants have regained strength, bolstered by the war in neighbouring Syria and widespread Sunni Arab anger with the federal government.

Fighting erupted near Ramadi on December 30, when security forces cleared a year-old Sunni protest camp.

The violence spread to Fallujah, and militants moved in and seized the city and parts of Ramadi after security forces withdrew.

Maliki had long sought the closure of the Ramadi protest camp, dubbing it a "headquarters for the leadership of Al-Qaeda".

But its removal has come at the cost of a sharp decline in Anbar's security situation just months ahead of Iraq's first elections since 2010.