Clashes first broke out in the Ramadi area on Monday as security forces tore down the country's main Sunni Arab anti-government protest camp near the city west of Baghdad, and continued for two days.
The violence also spread to nearby Fallujah, and security forces have since withdrawn from some areas of both Anbar province cities, which were once hubs of the insurgency that followed the 2003 US-led invasion of Iraq, giving the jihadists free rein.
A witness 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 ISIL and other areas are controlled by tribesmen," the ministry official said, referring to the provincial capital farther to the west.
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An AFP journalist in Ramadi saw dozens of trucks carrying heavily armed men in the east of the city, playing songs praising ISIL.
The militants also carried black flags of a type frequently flown by ISIL. The unrest has led to hardship in Ramadi.
"We are not leaving our homes because of what is happening," said one resident, Abdel Nasser.
"There is no food. Even if you manage to go to the market, you find nothing," he said.
Yesterday, militants and security forces in Ramadi clashed sporadically, with four police stations torched, but the fighting had subsided by today, the AFP journalist said.
In Fallujah, police abandoned most of their positions yesterday and militants burned some police stations, seized weapons and freed more than 100 prisoners, officers said.
However, army forces today remained outside both Ramadi and Fallujah, security officials said.
Maliki had long wanted the removal of the protest camp, which he called 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.
While the camp's closure has removed a physical sign of deep-seated grievances among Sunni Arabs, their complaints of being marginalised by the Shiite-led authorities and unfairly targeted by security forces remain unaddressed.