American troops in Iraq have been ordered to act less aggressively following warnings by the Iraqi Governing Council that people are turning against them.
Troops told to 'be polite'
But hours after the new battle was due to be tested, US forces killed at least two Iraqis whom they said were selling weapons in Saddam Hussein's home town, Tikrit, 175 kilometres (110 miles) north of Baghdad.
The BBC's Matthew Price, in Baghdad, said the soldiers spotted the men unloading weapons and bomb making equipment from a car and shot them - no questions asked.
In a separate incident, a US soldier was killed in western Baghdad on Thursday.
US military authorities have refused to say whether the soldier, who was on guard duty, died from a hostile attack.
Fifty-five Americans have died in such attacks since President George W Bush declared hostilities in Iraq largely over on 1 May.
Referring to the incident in Tikrit, US officials said a third man was captured at a hospital where he was being treated for wounds and a fourth, also believed to be wounded, was on the run.
"They began to pull additional weapons out of the trunk and
they became combatants at this point," military spokesman Lieutenant-Colonel Steve Russell said.
A cameraman Miran Jelenek for Reuters news agency saw the body of one man,
draped in a sheet, next to a pool of blood.
A red car, which troops said had been carrying Kalashnikov rifles and explosives, had windows shattered by gunfire and bloodstains on the seats.
The 150,000 US troops in Iraq have been told to be polite in their day-to-day dealings.
They have also been ordered to hand over control to Iraqi police once they have secured a town and when faced with a crisis, to hold their fire to the last.
The commander of the US-led forces in Iraq General Ricardo Sanchez suggested in an interview with The New York Times on Thursday that his troops' "iron-fisted" approach was provoking retaliation.
There are also reports that Iraqi resistance groups have quadrupled the bounty for killing an American soldier to $1,000.
"When you take a father in front of his family and put a bag over his head and put him on the ground, you have had a significant adverse effect on his dignity and respect in the eyes of his family," said General Sanchez.
He said the new military approach would concentrate more on co-operation with Iraqi political and religious leaders in an attempt to improve intelligence so that future searches could be more precisely targeted.
However, the BBC's correspondent in Baghdad Mike Donkin says for soldiers who have seen their comrades killed in the three months since war was supposed to have ended, restraint will be difficult.
Secretary of State Colin Powell has said the US-led military coalition may want to "stand back a little" and rely more on local forces to maintain security in the country.