The fire fight broke out in the middle of the day in a busy area

Both the US embassy in the Iraqi capital and the Iraqi interior ministry say they are looking into the incident.

The private security workers, who were employed by the US State Department, apparently opened fire after their convoy came under attack on Sunday.

At least 13 people were also injured in the shooting in a busy part of Baghdad.

It broke out at about 1230 local time on Nisour Square in the predominantly Sunni neighbourhood of Mansour, a police officer told the Associated Press news agency.

A witness said the shooting erupted after an explosion.

"We saw a convoy of SUVs passing in the street nearby. One minute later, we heard the sound of a bomb explosion followed by gunfire that lasted for 20 minutes between gunmen and the convoy people who were foreigners and dressed in civilian clothes.

"Everybody in the street started to flee immediately," Hussein Abdul-Abbas, a local shop owner, told AP.

Heavily armed

Another witness, Muhammad Hussein, saw his brother killed in the gunfight.

Critics say private security contractors are unregulated

Private contractors in Iraq

"I was driving behind my brother's car and suddenly there was an explosion and firing. I tried to figure out what was happening when I saw a black convoy ahead of us," he told the AFP news agency.

"Soon after I saw my brother slump in the car. I dragged him out of the car and tried to hide to avoid the firing but realised that he had been shot in the chest and was already dead," he said.

Thousands of private security staff are employed by businessmen, journalists and dignitaries in lawless Iraq.

They are often heavily armed, but critics say some are not properly trained - even trigger-happy - and are not accountable except to their employers.

Iraqi state television said Prime Minister Nouri Maliki had condemned the shooting.

Civilian toll

Sunday's violence followed the publication of a survey of Iraqis which suggested that up to 1.2m people might have died because of the conflict in Iraq.

A UK-based polling agency, Opinion Research Business (ORB), said it had extrapolated the figure by asking a random sample of 1,461 Iraqi adults how many people living in their household had died as a result of the violence rather than from natural causes.

The results lend weight to a 2006 survey of Iraqi households published by the Lancet, which suggested that about 655,000 Iraqi deaths were "a consequence of the war".

However, these estimates are both far higher than the running total of reported civilian deaths maintained by the campaign group Iraq Body Count which puts the figure at between 71,000 and 78,000.