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 on 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 their marginalisation and targeting.
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.
A police captain had earlier said fighters from ISIL, which operates in Syria as well, had advanced in early morning clashes into areas of central Ramadi and deployed snipers on one street.
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But Iraqi police, SWAT forces and allied tribesmen later battled ISIL militants in the area, Lieutenant Colonel Muthanna al-Hazza told AFP.
A police colonel said the army had re-entered areas of Fallujah, between Ramadi and Baghdad, but that around a quarter of the city remained under ISIL control.
However, a police lieutenant colonel said that while soldiers had deployed around the city, they had not yet entered. At least 14 people were killed on Monday and Tuesday in and near Ramadi.
Fallujah was the target of two major assaults after the 2003 invasion, in which American forces saw some of their heaviest fighting since the Vietnam War.
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.
Clashes erupted in the Ramadi area on Monday as security forces tore down the sprawling anti-government protest camp on a nearby highway.
The violence then spread to Fallujah, and a subsequent withdrawal of security forces from areas of both cities cleared the way for ISIL to move in.
ISIL is the latest incarnation of an al-Qaeda affiliate that lost ground from 2006, as Sunni tribesmen and former insurgents allied with US troops against jihadists.