The US Central Command said the soldier died of his injuries after being shot in the head inside Baghdad university campus.
A university lecturer who witnessed the shooting, Ali Jamah, told journalists: "The soldier entered the cafe on his own and when he was leaving, there was a shot and he fell to the ground."
"There was a man wearing university uniform who was carrying a pistol in his hand who fled,” he added.
Jamah said the soldier was completely motionless after the incident at the Jadriyah campus in the southwest of the city.
One student eyewitness, Abd Allah Saad, said he had seen the soldier lying on the ground, bleeding from a head wound.
US military spokeswoman Nicole Thompson said the shooting occurred at around 12:30 pm Baghdad time, adding that the soldier had been evacuated to hospital.
US forces closed the area down soon after the incident as troops began frisking people and searched vehicles leaving the campus.
A British officer at the scene, Captain Michael McBride, said the soldier had been accompanying officials from the US-led provisional authority who had gone to the campus to meet university officials.
In other developments, Aljazeera television reported four large explosions late on Sunday evening in Ramadi, west of Baghdad. It appears that rocket-propelled grenades were fired.
US military officials confirmed that their troops were involved in action in Ramadi.
A US military vehicle caught fire in the attack which occurred around 11:30 pm (1930 GMT), witnesses said, although they were unable to say if there had been any casualties.
US troops, backed by helicopters, returned fire and combed the
area, the witnesses said.
On Saturday, an explosion killed seven US-trained Iraqi police
recruits in the town amid an upsurge of attacks against US-led
|British journalist Richard Wild was|
killed outside Baghdad University
A British journalist was killed on Saturday also outside of Baghdad University. Witnesses say Richard Wild, 24 was crossing the street when a bullet shot from close range pierced the base of his skull.
The shootings have raised alarms as to whether his death was part of a wave of violent crime since the fall of Baghdad on 9 April, or part of a campaign by Iraqi resistance fighters.
Only minutes before his death, Wild had finished an interview with Dr Hussein Abbas Ali, director of the university’s national history museum.
“This makes me so sad. I think things are getting worse here,” he said.
Wild who was carrying nothing but a book when he left the campus, had told Ali he was taking a taxi back to his house in Baghdad’s Karradah neighbourhood.
Wild’s death raised the number of journalists killed to 14, since the US invaded Iraq on 20 March. Two other journalists, still listed as missing, are thought to have been killed during the war.