Iraqi officials said the helicopter seemed to have been shot down.
"If Iraq is to succeed, it will need both groups to come to terms and to work together for the benefit of all Iraqis"
Iceman, Atlanta, US
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Reuters quoted police Colonel Ali Nomas as saying that 300 to 350 armed men had been killed in the operation and dozens more arrested. Three Iraqi soldiers were killed and six more missing, and five policemen were killed.
Another 40 Iraqi police and soldiers were wounded.
The US military officially handed over responsibility for Najaf province to Iraqi security forces last month, withdrawing most US troops, to be recalled only to help in emergencies.
According to one Iraqi political source, hundreds of fighters, drawn from both Sunni and Shia communities, fought throughout Sunday and late into the night.
A Reuters reporter at the scene, 160km south of Baghdad, saw US tanks and heard blasts after dark and an Iraqi officer said F-16 jets were bombing the area.
Details of the day's fighting were sketchy and the origins of the fighters unclear. An Iraqi army source said some of the dead wore headbands declaring themselves a "Soldier of Heaven".
The political source said up to 1,000 fighters had been involved.
An Iraqi army source said they wore camouflage and appeared well organised.
The governor of Najaf province said the group had gathered in orchards near the city and had been planning to attack the main Shia clerical leadership on Monday.