Baghdad has expressed concern over a move to arm the Fallujah police force, staffed in part by members of the Sunni paramilitary force Sons of Iraq.
U.S. military officials said they may hand over security responsibility for Anbar province, where Fallujah is situated, as early as Monday.
With U.S. officials mulling over a phased departure from Iraq because of the long-term security agreement set to replace the expiring U.N. mandate, the fate of the 100,000-member Sons of Iraq force is a point of contention between Washington and Baghdad, the Iraqi daily Azzaman said.
Many officials in the Shiite-dominated government see the group as thugs, while U.S. strategists credit the organization with running al-Qaida elements out of the province.
The Sons of Iraq have faced persecution from Shiite militias throughout the country, and several key members of the organization have been the target of attacks and assassination attempts.
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