Iraqi forces and allied tribes had in the past few days been retaking areas of the Anbar provincial capital from the militants and anti-government tribal fighters, but the latest setback could prolong the standoff still further.
Parts of Ramadi and all of Fallujah, which lies just 60 kilometres from Baghdad, fell out of government control more than two weeks ago, the first time militants have exercised such open control in major cities since the insurgency that followed the 2003 US-led invasion.
Among the areas were two that police and allied tribesmen had wrested from them only days earlier.
Two policemen were killed and five others were wounded in the firefights, and three police vehicles were set ablaze, according to Dr Ahmed al-Ani at the city's main hospital.
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Sporadic clashes continued today in the affected neighbourhoods, while shelling struck the Andalus neighbourhood of central Ramadi, damaging houses in the area, a police officer said.
Gunfights also erupted in the Albubali area between Ramadi and Fallujah where security forces have repeatedly clashed with militants.
In Fallujah, government employees returned to work, but the city remained in the control of gunmen, according to an AFP journalist in the city.
The Iraqi army, which has largely stayed out of Fallujah, stayed on the city's eastern frontier today. Shelling in the city left two people wounded, witnesses said, while brief clashes could be heard in the city last day evening.