BAGHDAD (AFP) - Iraqi Prime Minister Nuri al-Maliki called on Wednesday for residents of the conflict-hit province of Anbar to "take a stand" against anti-government fighters, as the UN warned of worsening displacement.

His call came as government forces pressed an offensive against militants, including those affiliated with the Al-Qaeda-linked Islamic State of Iraq and the Levant (ISIL), who overran parts of the Anbar provincial capital Ramadi weeks ago.

Diplomats have urged Baghdad to foster political reconciliation to undercut support for the militants, but with elections looming in April, Mr Maliki and others have taken a hard line and focused on wide-ranging security operations.

"I ask the people of the province - the tribes, the notables, and all who live there - to be ready to take a stand, to take serious action against those dirty people, without making any sacrifices," Mr Maliki said in his weekly televised address.

He added, referring to Fallujah, another city in Anbar that is entirely in the control of anti-government fighters: "It is time to finish this subject, and end the presence of gangs in this city, and save the people from their evil."

Parts of Ramadi and all of Fallujah, both former insurgent bastions in Anbar west of Baghdad, have been in the hands of militants for weeks, the first time anti-government fighters have exercised such open control in Iraqi cities since the peak of the insurgency that followed the 2003 US-led invasion.

Soldiers, policemen and SWAT forces have combined with pro-government tribal allies in an offensive that continued on Wednesday against gunmen holding several neighbourhoods of Ramadi, an AFP journalist in the city said.

The army said in a statement that 13 militants were killed in firefights there.

In Fallujah, meanwhile, shelling in southern and central neighbourhoods left one person dead and 10 people wounded on Wednesday, a medic said.

Residents of the city blame the army for the shelling, but defence officials say the military is not responsible.

The government has tweaked its language in recent days from referring to all anti-government fighters in Anbar simply as Al-Qaeda, and now uses terms such as gangs.

And while Fallujah residents and tribal sheikhs have said ISIL has tightened its grip on the city in recent days, several other militant groups and anti-government tribes have also been involved in fighting government forces in both cities in Anbar.

Iraqi security forces, meanwhile, have recruited their own tribal allies to fight alongside them.