A doctor at a local hospital, who gave his name only as Assad, said six people were killed and seven were injured. Earlier, police officials said they opened fire after the protesters, who were demanding jobs, began throwing stones at the headquarters of the provincial government in the city.
A US military spokesperson said an Iraqi was shot dead by coalition forces as he hurled grenades during a demonstration.
"At 10:45am (0745 GMT), one Iraqi terrorist was killed during violent demonstrations in al-Amara," the spokesperson said.
"The terrorist had thrown two grenades. He was attempting to throw a third when he was shot by coalition forces."
But protestors in Amara claimed no one had attacked the soldiers and that the troops had opened fire first on the 600-person protest after they surrounded the city hall and demanded the local governor find them jobs.
"We came here to get a job, but instead of giving us a chance they opened fire on us," said Rada Hassun, 23. Another demonstrator, Mahmud al-Shati, 49, added: "We didn't do anything bad against the coalition forces and the police. They opened fire on us. We don't know why."
While in Tikrit, US soldiers shot and killed two Iraqi policemen embroiled in a family feud in the northern city of Kirkuk after mistaking them for assailants, the US military said on Saturday.
A military spokeswoman said soldiers from the 173rd Airborne Brigade were sent to respond to reports on Friday that two families were fighting. When they arrived, they saw two men carrying weapons and wearing long coats firing at a house.
"As the soldiers approached, the men attempted to flee," said Major Josslyn Aberle of the 4th Infantry Division.
"The soldiers pursued them, shouting warnings and firing warning shots but the men did not respond. They killed one outright and another died before reaching hospital," she said. A third man was unharmed.
"It later turned out all three were policemen," she said.
It is not the first time US forces have mistakenly killed members of the Iraqi police or other local security forces.
In December, three policemen were shot dead and two were wounded in the northern city of Kirkuk when US troops fired on a checkpoint after apparently mistaking the men for bandits.
And in September, American troops in the volatile town of Falluja accidentally killed 10 Iraqis belonging to the local police and another US-trained security force.
There are around 75,000 police in the new Iraqi force, which is being trained and funded by the United States.
As well as falling victim to US attacks, around 150 police have been killed in bombings or shootings carried out by anti-American insurgents who regard them as US collaborators.