The unrest in Anbar coupled with violence elsewhere in Iraq, which has already killed more than 600 people this month, has fuelled fears the country is slipping back into all-out sectarian war with little appetite for compromise among political leaders ahead of a general election scheduled for April.
UN chief Ban Ki-moon and other diplomats have urged Baghdad to pursue political reconciliation, but Iraqi Prime Minister Nuri al-Maliki has ruled out dialogue with militants and the authorities have instead trumpeted operations by the police and army.
The area, comprised of farmland and villages, lies between Ramadi and Fallujah, the two cities in the western desert province of Anbar at the centre of the crisis.
Security forces are also seeking to recover the bodies of eight of their own who have been killed in militant attacks.
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The air support which initially accompanied the operation has been withdrawn for fear that the militants have anti-aircraft weapons, two policemen told AFP.
A large swathe of Ramadi and all of Fallujah, both former insurgent bastions, fell out of government control late last month, marking the first time anti-government fighters have exercised such open control in major cities since the height of the insurgency that followed the US-led invasion of 2003.
The Al-Qaeda-linked Islamic State of Iraq and the Levant (ISIL) has been involved in the fighting alongside anti-government tribal fighters, while Baghdad has recruited its own allies among the province's powerful tribes.