Iraq's prime minister on Monday urged residents and tribes of Fallujah to "expel" Al Qaeda militants from this western city to avoid an all-out battle -- remarks that may signal an imminent military move to retake the former insurgent stronghold.

Nouri al-Maliki's message came as dozens of families were fleeing from Fallujah, 40 miles west of the Iraqi capital, Baghdad, in fear of a major showdown.

Iraqi government troops have surrounded the city, which lies in the western Sunni-dominated Anbar province and which was overrun by Al Qaeda fighters last week.

Al-Maliki did not say how he expects Fallujah residents and pro-government tribesmen to push the militants out. In his message, broadcast over state TV, al-Maliki also urged Iraqi troops to avoid targeting Fallujah's residential areas.

Along with Fallujah, Al Qaeda fighters last week also took control of most parts of the provincial capital of Ramadi.

Iraqi troops have since been trying to dislodge militants from the group, known as the Islamic State in Iraq and the Levant, or ISIL, from the two cities. On Sunday, fighting in Anbar killed at least 34 people, including 22 soldiers.

The recent gains by Al Qaeda in Iraq have been a blow to the country's Shiite-led government, as sectarian violence has escalated since the U.S. withdrawal. U.S. Secretary of State John Kerry said Sunday that Washington was "very, very concerned" by the fighting but would not send in American troops.

On Monday, the Iranian army's deputy chief-of-staff, Gen. Mohammad Hejazi, said Iran was also ready to help Iraq with military equipment and advisers, should Baghdad ask for it. Any Iranian help would exacerbate tensions as Iraqi Sunnis accuse Tehran of backing what they say are their Shiite-led government's unfair policies against them.

Fallujah residents said clashes continued into early morning Monday along the main highway that links the capital, Baghdad, to neighboring Syria and Jordan.

Al Qaeda fighters and their supporters are still controlling the center of the city where they can be seen on the streets and around government buildings. Al Qaeda black flags have been seen on government and police vehicles captured by the militants during the clashes.

In Ramadi, sporadic clashes were taking place in some parts of in and outside the city on Monday, residents there said. All residents in Anbar that talked to The Associated Press spoke on condition of anonymity, fearing for their own safety.

Dozens of families were fleeing the two cities to nearby towns, crammed in cars loaded with their belongings.

On Sunday, at least 22 soldiers and 12 civilians were killed, along with an unknown number of militants, and 58 people were wounded during clashes between Al Qaeda fighters on one side and the army and its allied tribesmen on the other.

Just hours earlier, Lt. Gen. Rasheed Fleih, who leads the Iraqi army's Anbar Military Command, told state TV that "two to three days" are needed to push the militants out of Fallujah and parts of Ramadi.

Tensions in Anbar have run high since Dec. 28, when Iraqi security forces arrested a Sunni lawmaker sought for terrorism charges. Two days later, the government dismantled a months-old, anti-government Sunni protest camp, sparking clashes with militants.

ISIL is also one of the strongest rebel units in neighboring Syria, where it has imposed a strict version of Islamic law in territories it holds in the civil war raging there. It also has kidnapped and killed dozens of people it deems critical of its rule. On Saturday, it claimed responsibility for a suicide car bombing in a Shiite-dominated neighborhood in Lebanon.

Iraq's Al Qaeda branch has fed on Sunni discontent and on Syria's civil war, in which mostly Sunni rebels fight the government of President Bashar Assad whose base is a Shiite offshoot sect.

Sectarian violence in Iraq spiked after the government staged a deadly crackdown on a Sunni protest camp last April. Militants have also targeted civilians, particularly in Shiite areas of Baghdad, with waves of coordinated car bombings and other deadly attacks.

According to the United Nations, Iraq had the highest annual death toll in 2013 since the worst of the sectarian bloodletting began to subside in 2007. The U.N. said violence killed 8,868 last year.