At least seven Iraqis are reported dead and 14 wounded in recent clashes with US troops in Karbala.
There have been anti-US demonstrations in Karbala
The US authorities said supporters of militant Shia cleric Moqtada Sadr had fired on troops from a holy shrine.
The fighting came as hundreds of people demonstrated in the city in protest against attacks on the shrines.
Iraq's most senior Shia cleric, Grand Ayatollah Ali al-Sistani, said on Tuesday all armed forces must be withdrawn from Karbala and Najaf.
He made the request in his first statement since Moqtada Sadr began an insurgency against US-led forces.
There was more violence further north; in the city of Mosul, one Iraqi policeman was killed in a bomb attack on a local official who escaped unhurt.
Outside Mosul, a British civilian contractor was killed on the road to Irbil.
Meanwhile, US military officials said an American marine died on Tuesday in a non-hostile incident in Anbar province, west of Baghdad. The US military had earlier said the marine was killed in action.
The latest clashes in Karbala began on Tuesday, during a US patrol, witnesses said. At least one Iraqi was killed in the initial fighting.
At least another six died on Wednesday as troops and militia fought near a checkpoint by the Imam Abbas shrine.
US Army First Armored Division spokesman Noel Gorospe said Mr Sadr's militia was operating from the Imam Hussein shrine.
They were firing with small arms, mortars and rocket-propelled grenades, mostly from the second floor, he said, adding that their presence appeared to be greater than on previous days.
There were pitched battles last week close to the sites.
Up to 15 US tanks briefly took up position near the two shrines on Sunday.