The switch follows clashes that began Monday with army and security forces, Middle East Online reported.
A ministry official said parts of Ramadi and more than half of Fallujah are controlled by the group Islamic State of Iraq and the Levant.
Other parts of the cities are in the hands of armed tribesmen, the official said.
Iraqi security forces tore down a major Sunni Arab anti-government protest site Monday, sparking clashes with Islamic militants. Sporadic fighting continued Wednesday, with four police stations being set ablaze.
In Fallujah, four police stations were burned Wednesday as police abandoned their positions.
A local tribal official said the Iraqi army shelled targets in Fallujah Thursday, killing one person and wounding nine others, the Anadolu Agency reported. The barrage began after tribesmen torched an army tank.