"Their deaths will not go unpunished. They have not died in vain," Bremer said in Baghdad as he attended the graduation of a new batch of 479 Iraqi police at the police academy.

Bremer described Wednesday's attacks by insurgents in and near Fallujah as "inexcusable and despicable".

But he vowed that the US-led coalition that toppled the ironfisted regime of Saddam Hussein almost a year ago will forge ahead with efforts to restore security in Iraq and hand over sovereignty to the Iraqis on July 1.

"They will not derail the march towards stability and democracy," Bremer told the new police cadets.

Reaction was also fierce from Washington, where White House spokesman Scott McClellan said: "We condemn these attacks on the strongest possible terms".

In Fallujah, schools and shops were open on Thursday and burn marks on the surface of the main street were the only evidence of the gruesome deaths of the four employees of the private US firm Blackwater Security Consulting, AFP correspondents said.

One witness said that what remained of the charred bodies after they were dragged from their cars, mutilated and strung from a bridge had been "cut up into pieces, with parts thrown into the river or to the dogs".

Residents also took away the carcasses of the two four-wheel-drive vehicles that had been ambushed and set on fire by gunmen, burning the occupants to death, the witness said.

US marines, who were seen Wednesday at the eastern entrance of Fallujah, were nowhere in sight while Iraqi police and paramilitary defence units manned a checkpoint to search cars entering the town and control identities.

The previous evening, hours after the killings, crowds were still celebrating in the streets, with people firing in the air and distributing candies.

They shouted, "Down with the occupation, down with America" and "long live Islam."

"The death of each one of these people is worth 10 Iraqi lives. This is our only deterrence to the (US-led) occupation of Iraq," Nayef, a car merchant who declined to give his surname, told AFP on Thursday.

The previous day a man at the scene, his face hidden by a scarf, vowed that "Fallujah will be the cemetery of the Americans".

Meanwhile the US-backed paramilitary Iraqi Civil Defence Corps urged restraint in Fallujah in a statement handed out to residents late Wednesday.

"An agreement has been negotiated with the occupation forces to lift the siege of Fallujah and to withdraw. We are hoping you will cooperate to protect Fallujah and guarantee its security," the message said.

The death of the four civilians coincided with a roadside bomb blast that killed five US soldiers near the military base in Habbaniya, just west of Fallujah.

It is thought to be the worst single incident involving coalition troops since a US military helicopter was downed on January 8 near Fallujah, killing all nine people aboard.

The latest deaths brought to 291 the number of US soldiers killed in action since US President George W. Bush declared major hostilities over on May 1, according to an AFP toll.

In other violence Thursday one US soldier was wounded when his convoy hit a roadside bomb in northwest Baghdad, an Iraqi police officer said. The US military did not immediately confirm the report.

And in the northern city of Kirkuk three soldiers were wounded when five Katyusha rockets struck their base located in a local airport just west of the city early Thursday, a US officer said.