British troops have been involved in a violent confrontation with protesters in the southern Iraqi town of Amarah.
British forces have faced less unrest in southern Iraq
At least five people are reported to have been killed when troops and Iraqi police fired on crowds demanding jobs.
UK military officials confirmed at least one man was shot dead by a British soldier, as he was about to throw a grenade at troops.
Amarah, a Shia Muslim town under UK control, has seen much less unrest than Sunni Muslim areas around Baghdad.
Earlier, US soldiers shot and killed two Iraqi police officers after intervening in an apparent family feud in the northern city of Kirkuk.
Witnesses in Amarah say the crowd had been demonstrating against the recently elected governor and the lack of jobs in the region.
They began throwing stones and explosive devices at the Iraqi police who shot at protesters, killing four, reports said.
British soldiers moved in to try to restore order and also opened fire.
Coalition officials said one man had come forward and thrown two grenades and, as he was trying to throw a third, he was shot by a British soldier.
Another man, also said to have been armed with grenades, was shot and injured, the UK Ministry of Defence said.
"It is our understanding that there have been six casualties - five fatalities and one injured," a spokesman said.
"We believe that [coalition forces] killed one and injured another. We do not have any further information on the other four fatalities."
An eyewitness said there were big bangs and shockwaves, but it was confused and not clear whether it was Iraqi police or protesters who began firing first.
The hospital in Amarah earlier reported six people killed and a spokesman said 11 had been injured.
On Tuesday, four Iraqi army veterans were wounded in the main southern city of Basra when police opened fire during a demonstration about unpaid stipends.
A military spokeswoman in Kirkuk said the Iraqi policemen who were killed there did not identify themselves to an American patrol, despite repeated requests and the firing of warning shots.
Soldiers from the 173rd Airborne Brigade had been sent to the Rahima neighbourhood to respond to reports on Friday that two families were fighting, the spokeswoman said.
Tensions have been rising in Kirkuk
When they arrived, they saw two men firing at a house, the spokesman said, and as they approached the two tried to flee.
"The soldiers pursued them, shouting and firing warning shots, but the men did not respond. They killed one outright and another died before reaching hospital," she said.
Last month, three Iraqi policemen were killed and two wounded in Kirkuk when US soldiers mistook them for bandits.