The deaths sparked angry protests in Kut and calls for an investigation
A US raid in the south of Iraq, in which two people died, was a crime and those responsible should be tried, says Iraqi Prime Minister Nouri Maliki.
He said the raid in the town of Kut was a breach of the security pact governing US military actions in the country.
The US has said the raid was carried out in full agreement with the Iraqis.
The BBC's Jim Muir in Baghdad says it is the most serious dispute between the US and Iraq since the agreement came into force at the start of the year.
One senior local official said the actions had rendered the pact "meaningless".
US forces stormed buildings in Wasit province early on Sunday morning.
A policeman and a woman were shot dead and six people detained.
The US military said the raid, against a weapons smuggler and "network financier", had been "fully coordinated and approved by the Iraqi government".
They said soldiers had shot and killed "an individual with a weapon" outside the house and that the woman who died had "moved into the line of fire".
Two senior Iraqi army officers were arrested for permitting an American operation to go ahead without the knowledge of the Iraqi authorities.
In a statement read on state TV, Mr Maliki said he condemned the killings as a "breach of the security pact".
He called on the US to "release the detainees and hand over those responsible for this crime to the courts".
The incident caused uproar in Wasit, where provincial governor Latif Hamad al-Turfah echoed Mr Maliki's condemnation.
He said local government and officials had been "surprised that these forces carried out the raid in breach of the agreement signed between the Iraqi and US governments".
The chairman of the provincial council, Mahmud Abd al-Rida, said the raid had embodied the "meaning of the occupation".
"Their claim of friendship and early withdrawal from our dear land, according to the security agreement signed by the two Iraqi and US parties, is meaningless," he said.
The complicated Status of Forces Agreement was signed in November last year and came into force in early 2009.
It requires all military operations in Iraq to have the government's approval and allows for US soldiers to face trial if they commit crimes off base.
The US currently has more than 140,000 troops in Iraq, and combat troops are due to pull out of Iraq's cities by the end of June.