Iraqi forces backed by tanks battled militants Thursday in Anbar, where fighting has displaced thousands and sparked warnings of rights abuses and fears the crisis could take weeks to resolve.

They also faced violence in the capital, where a suicide bomber targeted an army recruiting centre, killing 23 people and wounding 30.

The United Nations and non-government organisations have warned that civilians lack access to key supplies as the government blockades Fallujah and parts of the nearby Anbar provincial capital Ramadi, west of Baghdad, which were seized by militants last week.

Washington has piled pressure on Iraq to focus on political reconciliation as well as military operations to resolve the standoff.

The Anbar crisis and a protracted surge in nationwide violence are among the biggest threats faced by Prime Minister Nuri al-Maliki during his eight years in office, and come just months before the first general election in four years.

On Thursday, security forces engaged in heavy fighting with Al-Qaeda-linked militants in the Albubali area, between Ramadi and Fallujah, a police officer said.

Eventually, tank and helicopter fire destroyed a school and several houses from which militants had been firing, ending the fighting, the officer said.

Human Rights Watch (HRW) condemned abuses by all sides in the Anbar clashes, criticising government forces for allegedly using indiscriminate mortar fire in civilian neighbourhoods, and militants for deploying in and attacking from populated areas.

"Apparently unlawful methods of fighting by all sides have caused civilian casualties and severe property damage," the New York-based group said.

With their seizure of Fallujah and parts of Ramadi, this is the first time militants have exercised such open control in major cities since the insurgency that followed the 2003 US-led invasion.

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

At the same time, security forces have recruited their own tribal allies in the fighting that has raged in Anbar for over 10 days and killed more than 250 people.

The Iraqi Red Crescent said it had provided humanitarian assistance to more than 8,000 families across Anbar but that upwards of 13,000 had fled. The UN said it had also managed to provide critical supplies.

Some families have sought refuge in the neighbouring province of Karbala and, according to HRW, as far away as the northern Kurdish region.

In Washington, US Vice President Joe Biden called Maliki for the second time this week, raising pressure on the premier over the unrest.

He urged Maliki to "continue the Iraqi government's outreach to local, tribal, and national leaders," following the loss of Fallujah, a White House statement said.

Political reconciliation, military action

Spokesman Jay Carney said Washington was pressing Maliki, a Shiite, to focus on political reconciliation as well as acting militarily to expel militant groups from Fallujah and Ramadi.

A senior US official warned that the crisis could take several weeks to resolve.

"We're encouraging a patient and deliberate approach," the official said, speaking on condition of anonymity. "I think weeks would be prudent."

Traffic police have returned to Fallujah's streets, some shops have reopened and more cars could be seen, but the city was still rocked by clashes and shelling, and ISIL has urged Sunnis to keep fighting the government.

An Iraqi military spokesman said an assault on Fallujah was on hold for fear of civilian casualties.

Attacking the Sunni-majority city would be a significant test for security forces, who have yet to undertake such a major operation without the backing of US troops.

It would also be extremely sensitive politically, as it would inflame already high tensions between the Sunni Arab minority and the Shiite-led government.

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

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