The Reuters photographer reported that the boys were no older than 12 years of age.
A US military spokesman said: "We are looking into the circumstances of what caused the incident," and said it was unclear if the children had been hurt from gunfire or shrapnel from any explosion.
The statement said soldiers on the western side of the Tigris had engaged two armed men trying to smuggle weapons across the river by boat.
The men fled to the eastern side, where they were joined by three other gunmen, the military said.
"Peace in Iraq will happen when citizens realise that they can express their ideas and views more effectively... than with violence"
JBernar5, Toledo, USA
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"After an initial firefight, the five gunmen took cover in a bunker and a large shipping container along the river bank. They continued firing across the river at the troops," the statement said.
"The soldiers returned fire with small arms, and eventually used tank rounds to destroy the bunker and end the attack," the statement continued.
The Reuters photographer said the dead boy lay behind the container, which had been torn open.
He saw about 30 US soldiers and several Stryker armoured vehicles, backed up by two helicopters, on the western side of the river.
The two wounded boys were taken in an Iraqi army vehicle to hospital, along with the body of the boy who had died at the scene.
The incident followed the launch of a final crackdown by US and Iraqi forces to avert a civil war.
Earlier on Friday, the US military said it was investigating whether civilians, including two children, were killed during another fierce gun battle in the western town of Ramadi on Wednesday.