Witnesses said US soldiers fired randomly after their vehicle was hit by a roadside bomb. The soldiers then raided houses in the area.
A spokesman for the US-led coalition said Ukrainian soldiers in the area had fired warning shots when protesters started to move towards the troops, but did not report any casualties.
"There was a demonstration of 1,000 people. They started to be offensive and moving forward and shouting, so the Ukrainians fired some warning shots in the air," said Polish Lieutenant-Colonel Robert Strzelecki.
Reuters television footage showed cars and front doors pierced by bullets. One man showed bullet holes in his kitchen pots and pans, as well as a shattered television screen.
"There were only innocent children here," he said. "What did they think, that Saddam Hussein was here?"
Ramadi is one of the flashpoint towns west of Baghdad where US convoys regularly come under attack and soldiers often carry out raids looking for insurgents in the town.
US occupation soldier killed
Elsewhere the US military said a bomb went off as a convoy made its way past central Baghdad, killing one soldier and injuring two others attached to the 1st Armoured Division.
The latest death brings to 343 the number of US soldiers killed in action in Iraq since the start of the war in March.
Monday's explosion underlined how dangerous occupied Iraq remains even after the capture of former ruler Saddam Hussein.
US-led occupation forces have failed to stamp out resistance attacks. They continue with the same degree of ferocity as before, though the number of daily attacks have marginally dropped.
Meanwhile, US troops killed seven men in a gunbattle with an armed gang trying to steal fuel from a pipeline near the Iraqi town of Samarra.
According to a US army spokesman, an Iraqi citizen led US troops late on Sunday to a group of about 40 men, armed with AK-47 assault rifles, who were trying to siphon fuel from a stretch of pipeline 18km north of Samarra.
US officials say fuel smuggling has
resulted in chronic shortages
The bandits, who had between 10 and 15 trucks, shot at the soldiers as they came forward to capture them, Sergeant Robert Cargie of the 4th Infantry Division told reporters in Tikrit.
Troops returned fire with rifles and a 125mm cannon on a Bradley fighting vehicle, killing seven of the thieves.
"Three fuel trucks and one transport truck were destroyed," Cargie said. He said the thieves did not succeed in breaching the pipeline.
Officials in the US-led administration say rampant fuel smuggling has contributed to chronic fuel shortages. Iraq has the world's second-biggest oil reserves.
Amara protests continue
Meanwhile, more than 200 demonstrators took to the streets of the southern city of Amara on Monday after a weekend of unrest in which six Iraqis died when British troops and Iraqi police opened fire on protesters.
The protesters were blocked by British soldiers from advancing on a local government headquarters, the scene of demonstrations on Saturday and Sunday over chronic unemployment, witnesses said.
A British military spokesman confirmed that protesters had regrouped in the city and said troops were monitoring what was so far a peaceful gathering.
Six Iraqis were killed when troops
opened fire on Amara demonstrators
Soldiers had earlier closed a bridge near the government buildings and searched passers-by as tensions remained high in the city.
Foot patrols had also been increased in the area from which Iraqi police had withdrawn after accusations they opened fire on the crowd without warning on Saturday.
British army helicopters had since dawn been hovering over the centre of the Shia city about 365km from Baghdad.
On Sunday, soldiers baton-charged a couple of hundred Iraqis who pelted them with rocks in Amara. No one was reported wounded and a protest later reassembled, before police fired in the air and arrested two men.