In Baghdad, US ground forces and helicopters opened fire at former Iraqi soldiers, who were heading to the Conference Palace - where the US-backed Iraqi Governing Council is based - to stage a protest over unpaid salaries, our correspondent said.
A number of former Iraqi soldiers were injured in the shooting according to eyewitnesses.
Another Iraqi was killed during demonstrations in the southern city of Basra, a British military spokesman said.
"One Iraqi was shot by a coalition soldier during protests. This is a serious matter and we are investigating," Major Niall Greenwood told Reuters news agency.
Dr Abbas Jaffer, a doctor at Yarmuk Hospital where the victims of the Baghdad fighting were taken, said six Iraqis were brought in with gunshot wounds.
The doctor said one "was dead on arrival with a bullet to the head" but did not identify him. Two of the five others were in serious condition with chest wounds, he said.
The US military, which earlier reported two American soldiers had been wounded in the clash, could not confirm the toll among Iraqis. "We don't take Iraqi casualties," said a spokeswoman who asked not to be named.
The US military brought in tanks to quell the protests
Meanwhile, Italian troops opened fire on Saturday at Iraqi protesters in al-Nasiriya, who had also gathered to receive their salaries, our correspondent in that city reported.
A US soldier was killed and another wounded late on Friday in another incident in southwest Baghdad, according to the US military.
In a statement released on Saturday, the US said soldiers from the 4th Infantry Division were attacked at 11.45pm (2045 GMT) by at least one rocket-propelled grenade and small arms fire.
Three attacks were launched overnight on Iraqi police officials and occupation forces in the northern Iraqi oil centre of Kirkuk.
A grenade was hurled at the home of the city's police chief, Sabah Bahlul Karatun, at 12 noon (0900 GMT) on Friday, said Khattab Abd Allah, director of Kirkuk's emergency police unit.
The blast blew out the windows of Karatun's home, but nobody was there at the time, Abd Allah said.
A security source reported eight explosions on the US military airbase in Kirkuk.
Ten minutes later, an unknown assailant threw a grenade at the Al-Rashid kebab restaurant popular with US troops in Kirkuk, but it was not clear if anyone was injured.
The Al-Mikdad police station also came under attack when gunmen pulled up in a car and sprayed gunfire, provoking a 10-minute shoot-out. The car then sped away and no one was hurt.
The US military had no immediate comment on the incidents.
A security source, on condition of anonymity, also reported eight explosions at 11pm (2000 GMT) on the US military airbase in Kirkuk.
There was another round of explosives at midnight but the army called them detonations of old Iraqi munitions left over from Saddam Hussein's era.
However, the security source said the army usually explodes old Iraqi munitions between noon and 1pm daily.
It was the third straight night of fighting in this volatile city
where ethnic tensions seethe under the surface.
Kirkuk seethes with ethnic tension
The US military said two Iraqis were killed by an explosion in Kirkuk late on Thursday, but would not confirm reports by local officials that they were human bombers.
The blast went off as US troops approached two Iraqis trying to plant an "improvised explosive device (IED)", said a military spokesman who asked not to be named.
Civil defence officials in the northern oil centre had earlier reported two bombers blew themselves up outside a dry cleaners' used by US troops in Kirkuk.
They reported no American casualties in the blasts, which came after six other explosions rocked the city, leaving at least two soldiers wounded, officials said.
The US army had no report on the other explosions.
Meanwhile, US troops arrested two Iraqi gunmen on Friday after a firefight in Al-Khalidiya, 80km west of Baghdad.
The fight was sparked by a landmine explosion that destroyed a military vehicle, a witness said.
The US military had no immediate comment on the incident.
Al-Khalidiya falls within the western Anbar province, home to the flashpoint towns of Falluja and Ramadi, a major battlefield in the fighting between US forces and resistance fighters.
Iraqi police arrested Aljazeera cameraman Salah Hassan on Friday while he was filming a pro-Saddam demonstration in Shahraban town, near Baqubah.
He was charged with possessing a large amount of money with which to organise demonstrations, but according to Aljazeera reports he was only carrying $500.