Air supportair support was called in by the Iraqi army following the "positive identification of ... illegally armed militia men using shoulder-fired rocket-propelled grenades".
The US military said
"The chances of success [in Iraq] are essentially zero because the Iraqi people have no voice"
Non Sequitur, Cadiz, Spain
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Local police were warned to stay inside and unarmed during the operation.
The raids came ahead of demonstrations planned for Monday by supporters of al-Sadr to mark four years since the fall of Baghdad.
The Iraqi military source said clashes were pitting Iraqi and US forces against armed men in Diwaniya's Salim Street and southern areas of the city including the Nahda and Wahda districts.
A curfew continued in Diwaniya for a second day and hospitals called in doctors to report for duty, the Iraqi army source added.
US-backed Iraqi forces swept through the city on Friday, arresting nearly 30 people and killing three fighters as part of the crackdown aimed at Shia groups.
The military said the operation was intended to disrupt militia activity and return control of the city south of Baghdad to the government.
Over the past year, Diwaniya has seen repeated clashes between the security forces and Shia militias.
Last August, nearly two dozen Iraqi soldiers and dozens of militiamen were killed in the deadliest bout of fighting.
Meanwhile, Hoshiyar Zebari, Iraq's foreign minister, announced that a meeting on stabilising the country would be held in Egypt in the first week of May.
The meeting between Iraq, its neighbours and other nations follows talks in March. Zebari also said that an international conference on a five-year plan for the reconstruction of Iraq would be held at the same time.