FALLUJAH, Iraq -- A U.S. general vowed an "overwhelming" response to the murder and mutilation of four American contractors, but U.S. troops stayed out of this anti-American city Thursday and fearful Iraqi police took no action.

Residents said they were ready to take on the Americans if they try to enter Fallujah, where schools and shops remained open a day after insurgents ambushed the contractors' SUVs and mobs strung up two of their charred corpses on an iron bridge spanning the Euphrates River.

"We wish that they would try to enter Fallujah so we'd let hell break loose," Ahmed al-Dulaimi said. "We will not let any foreigner enter Fallujah," said Sameer Sami. "Yesterday's attack is proof of how much we hate the Americans."

Near Fallujah on Thursday, insurgents set off a bomb beside a U.S. military patrol, wounding three troops. Associated Press Television News footage showed smoke and fire pouring from an abandoned Humvee on the side of a road.

In Ramadi, west of Fallujah, six Iraqi civilians died and four were wounded Wednesday evening in a car bombing at a market, said Lt. Col. Steve Murray, a coalition spokesman.

Also Thursday, two explosions near a U.S.-escorted fuel convoy in Baghdad wounded at least one Iraqi. APTN footage showed U.S. soldiers putting a wounded person on a stretcher in an armored vehicle.

U.S. troops stayed out of Fallujah on Thursday despite pledges from a military commander to stamp out resistance in a city that is home to militant forces who appear to enjoy the support -- or at least acquiescence -- of a significant part of the population. The city was a stronghold of support for Saddam Hussein, who was ousted in the invasion a year ago.

"We will pacify that city. ... It will be at the time and place of our choosing," Brig. Gen. Mark Kimmitt said, pledging to hunt down those who carried out Wednesday's killings, which were reminiscent of the televised abuse of the corpses of American soldiers in Somalia in 1993.

Kimmitt promised a response that will be "deliberate" and "overwhelming," and said troops didn't respond at the time for fear of ambushes or the insurgents might use of civilians as human shields. He also said U.S. forces took into account that the contractors were already dead.

"We are not going to do a pell-mell rush into the city," he said. "A pre-emptive attack into the city could have taken a bad situation and made it even worse."

Fallujah, 35 miles west of Baghdad, has been the scene of some of the worst violence since the beginning of the U.S.-led occupation a year ago.

Last month, U.S. Marines took over authority of Fallujah and surrounding areas from the 82nd Airborne Division and conducted patrols that led to fierce firefights in the city.

The Marines enter Fallujah only on days when they conduct a military operation in the city. The Marines were apparently not in Fallujah on Wednesday when mobs dragged the mutilated and burned bodies of the four Americans through the streets.

Apparently fearful Iraqi police in the city stayed away from the mobs, and picked up the bodies hours later only at the request of American troops.

'None of our business'

On Thursday, police manned roadside checkpoints and remained at their posts but were not conducting raids or operations related to the killings. Two officers told The Associated Press they were afraid, while a third said: "Why should we interfere? It's none of our business."

It was unclear why the American contractors were traveling unescorted in such a dangerous area. The four worked for Blackwater Security Consulting of Moyock, N.C., which provides training and guard services to customers around the world. Blackwater is a government subcontractor providing security for the delivery of food in the Fallujah area.

Iraq's administrator, L. Paul Bremer, condemned the killings as well as the combat deaths of five American soldiers on the same day, and said "their deaths will not go unpunished."

"Yesterday's events in Fallujah are dramatic examples of the ongoing struggle between human dignity and barbarism," Bremer said at a ceremony for police cadets in Baghdad. "The acts we have seen were despicable and inexcusable. ... They violate the tenets of all religions, including Islam."

Samir Shaker Mahmoud, a member of the U.S.-appointed Iraqi Governing Council, said he hoped the response of the U.S. military in the area would not be based on "revenge."

Iraqi Interior Minister Nori al Badran also promised to send forces into Fallujah but did not say when.

"We were shocked because our Islamic beliefs reject such behavior," police Lt. Salah Abdullah said in a reference to the abuse of the bodies.

Major newspapers in the United States ran graphic photos Thursday of the charred bodies, while the images were largely shunned by American television as too horrific.

Overseas, broadcasters and newspapers carried the gruesome images, though some London tabloids blurred the photos and Arab television obscured more gruesome footage.

Some European newspapers speculated about a quicker U.S. troop withdrawal and others said it could serve as a new standard for attacks.

But Secretary of State Colin Powell said the United States would not be "run out" of Iraq.

"America has the ability to stay, fight an enemy and defeat an enemy," Powell, who was attending a donor conference in Berlin for the rebuilding of Afghanistan, said in an interview on German ZDF television.