Violence, which surged after deadly crackdown on protests, claimed more than 8,000 lives, mostly civilians, in 2013.
Heavy fighting raged between the Iraqi military and Sunni fighters in Anbar province, after gunmen seized control of several police stations there.
An interior ministry official told AFP news agency on Thursday that al-Qaeda-linked fighters were in control of large parts of Anbar’s Fallujah and Ramadi cities.
“Half of Fallujah is in the hands of ISIL (the Qaeda-linked Islamic State of Iraq and the Levant) group, and the other half is in the control of” armed tribesmen, the official said.
A witness in the city west of Baghdad said that fighters had set up checkpoints each manned by six to seven people in central and south Fallujah.
“In Ramadi, it is similar – some areas are controlled by ISIL and other areas are controlled by” tribesmen, the interior ministry official said, referring to the Anbar provincial capital, which lies farther to the west.
On Wednesday, gunmen attacked the main police station in Fallujah and ordered its staff to leave, before raiding its armoury and freeing 101 prisoners from its cells, police said. Other police stations in the city were torched by fighters as most police abandoned their posts.
Iraqi Prime Minister Nouri al-Maliki on Wednesday ordered reinforcements to the mainly Sunni Arab province to tackle attacks by armed groups, reversing a decision just a day earlier to withdraw soldiers from Anbar cities and hand over control to police.
The fighting broke out on Monday, when security forces tore down a year-old Sunni Arab protest camp outside the provincial capital Ramadi.
The removal of the protest camp was seen as a victory for Maliki, who had long wanted it gone and had termed it a “headquarters for the leadership of al-Qaeda”.
But it has carried a high price, not only in terms of the deteriorating security situation in Anbar, but also in the political fallout.
Forty-four MPs announced on Monday that they had submitted their resignations, and called for “the withdrawal of the army from the cities and the release of MP Ahmed al-Alwani.”
Alwani, a Sunni Arab MP who was a leading supporters of the protest camp, was arrested in a raid on his Ramadi home on Saturday in which his brother, five guards and a security forces member died.
Protests broke out in Sunni Arab-majority areas of Iraq late last year after the arrest of guards of then-finance minister Rafa al-Essawi, an influential Sunni Arab, on terrorism charges.
The arrests were seen by Sunnis as yet another example of the Shia-led government targeting their leaders.