Violence first erupted on Monday when militants clashed with security forces in country's main anti-government protest camp near Ramadi, west of Baghdad.
The clashes spread to Ramadi and then to Fallujah, where they continued for another two days.
Security forces have since withdrawn from some areas of the two cities in Anbar province.
Iraqi Television aired a video showing country’s air force bombing a militant base in the area, as the army continues its operations to curb the insurgency.
"Half of Fallujah is in the hands of ISIS (the Qaeda-linked Islamic State of Iraq and the Levant) group, and the other half is in the control of" armed tribesmen, an interior ministry official told AFP.
A witness in the city west of Baghdad said that militants 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 ISIS and other areas are controlled by" tribesmen, the interior ministry official said, referring to the provincial capital farther to the west.
On Wednesday, militants in Ramadi sporadically clashed with security forces and torched four police stations, but the fighting had subsided by Thursday, the AFP journalist said.
The violence had also spread to Fallujah, where police abandoned most of their positions on Wednesday and militants burned some police stations, seized weapons and freed over 100 prisoners, officers said.
Iraqi Prime Minister Nuri al-Maliki had long wanted the removal of the protest camp, which he termed a "headquarters for the leadership of Al-Qaeda," but doing so has come at the cost of a sharp decline in the security situation in Anbar.
SHI/SHI