Iraqi forces backed by tanks are battling militants in Anbar, where fighting has displaced thousands and sparked warnings of rights abuses and fears the crisis could take weeks to resolve.
They also faced violence in the capital, where a suicide bomber targeted an army recruiting centre, killing 23 people and wounding 30.
The United Nations and non-government organisations have warned that civilians lack access to key supplies as the government blockades Fallujah and parts of the nearby Anbar provincial capital Ramadi, west of Baghdad, which were seized by militants last week.
Washington has piled pressure on Iraq to focus on political reconciliation as well as military operations to resolve the standoff.
The Anbar crisis and a protracted surge in nationwide violence are among the biggest threats faced by Prime Minister Nuri al-Maliki during his eight years in office, and come just months before the first general election in four years.
On Thursday, security forces engaged in heavy fighting with Al-Qaeda-linked militants in the Albubali area, between Ramadi and Fallujah, a police officer said.
Eventually, tank and helicopter fire destroyed a school and several houses from which militants had been firing, ending the fighting, the officer said.
Human Rights Watch (HRW) condemned abuses by all sides in the Anbar clashes, criticising government forces for allegedly using indiscriminate mortar fire in civilian neighbourhoods, and militants for deploying in and attacking from populated areas.
The Iraqi Red Crescent said it had provided humanitarian assistance to more than 8000 families across Anbar but that upwards of 13,000 had fled. The UN said it had also managed to provide critical supplies.
Some families have sought refuge in the neighbouring province of Karbala and, according to HRW, as far away as the northern Kurdish region.
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