Parts of Ramadi and Fallujah, west of Baghdad, have been held by militants for days, harkening back to the years after the 2003 US-led invasion when both cities were insurgent strongholds.
Fighting began in the Ramadi area Monday, when security forces removed the main anti-government protest camp set up after demonstrations broke out in late 2012 against what Sunni Arabs say is the marginalisation and targeting of their community.
Anger at the Shiite-led government among the Sunni minority is seen as one of the main drivers of the worst violence to hit Iraq in five years.
At least 32 civilians and 71 ISIL fighters died in the clashes, the officials said, adding that they did not know how many police and tribesmen were killed.
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Hundreds of gunmen, some of them carrying the black flags often flown by jihadists, gathered at outdoor weekly Muslim prayers in central Fallujah, a witness said.
At least 14 people were killed on Monday and Tuesday in and near Ramadi, while the tolls from the following two days were not immediately clear.
American troops fought for years, aided by Sunni tribesmen in the Sahwa militia forces from late 2006, to wrest control of Anbar from militants.
During their time in Iraq, US forces suffered almost one-third of their total fatalities in Anbar, according to independent website icasualties.Org.
But two years after US forces withdrew from Iraq, the power of militants in the province is again on the rise.
Clashes erupted in the Ramadi area on Monday as security forces tore down the sprawling anti-government protest camp on a nearby highway.