A third was beaten by the Americans in the incident on Saturday, a survivor said.
The three Iraqi officers were firing from their unmarked police car at a vehicle they were chasing when the soldiers opened fire on them in a western suburb of the capital, Sergeant Hamza Hilal Nahi, who said he was driving the car, told Agence France Presse.
Lieutenant Colonel Muayad Farhan, deputy head of Al-Yarmuk police station where the dead officers were based, confirmed that two of his officers had been shot by coalition forces.
The US military said it was aware of an incident, but unable to provide information. However,army spokesman Staff Sergeant JJ Johnson said on Sunday there had been a case of "blue on blue" on Saturday, a term for an incident where friendly forces fire on one another.
As the Al-Yarmuk deputy police chief spoke to AFP on Monday, two US military police officers came to offer their condolences to him.
They asked not to be named, but said they believed the two officers had been shot by US troops after being mistaken for attackers.
Bringing more Iraqi police onto the front line in lawless Baghdad is seen as a top priority among Iraqi citizens.
Results released this week from a poll of 2,600 Iraqis show 39 percent of respondents say giving Iraqi police greater responsibility for maintaining security is the number one step towards greater stability.