An Iraqi provincial governor Saturday gave militants controlling a city near Baghdad one week to surrender as government forces made steady progress in an effort to end a weeks-long crisis.

The Anbar governor's ultimatum was directed at anti-government fighters who have held Fallujah for more than a month.

It comes amid a protracted surge in violence with security forces grappling with near-daily attacks nationwide in addition to the fighting in the western desert province.

Analysts and diplomats have called for the Shiite-led government to address Sunni grievances in order to undermine support for militants, but with April elections looming, Prime Minister Nuri al-Maliki has taken a hard line.

"People of Anbar, criminals have kidnapped Fallujah," Governor Ahmed al-Dulaimi said in a statement.

"But, I swear to God, we will achieve victory against injustice and Fallujah will return to normal."

Dulaimi gave anti-government fighters a week to lay down their arms and promised them amnesty, but said the authorities would not negotiate with the Islamic State of Iraq and the Levant (ISIL), a powerful jihadist group he said was comprised of "killers and criminals".

Fallujah and provincial capital Ramadi have for weeks been hit by conflict, and while government forces have made steady progress in retaking militant-held areas of Ramadi, they have largely stayed out of Fallujah for fear that an incursion would spark a drawn-out urban conflict with high numbers of casualties.

The city was a bastion of the Sunni insurgency following the 2003 US-led invasion, and American troops there fought some of their costliest battles since the Vietnam War.

In Ramadi, meanwhile, police Lieutenant Colonel Hamid Shandukh said security forces had defused upwards of 400 roadside bombs, including dozens used to booby-trap houses.

Tribal leader Ahmed Abu Risha, who years ago sided with the US military and founded the Awakening movement of tribal militias against Al-Qaeda, a day earlier held a news conference during which he showed what he said were bills distributed by ISIL as their own currency.

The 100-guinea note bore the likeness of former Al-Qaeda chief Osama bin Laden on one side, and the two World Trade Centre towers attacked by the group on September 11, 2001 on the other.

The Anbar stand-off has prompted more than 140,000 people to flee their homes, the UN refugee agency said last month, calling it the worst displacement in Iraq since the peak of sectarian fighting between 2006 and 2008.