FALLUJAH, Iraq – Insurgents tried to break through the American cordon surrounding Fallujah yesterday as American forces launched an offensive against concentrations of militants in the south of the city. Some 600 insurgents, 18 American troops, and five Iraqi soldiers have been killed in the four-day assault, the American military said.

American troops, meanwhile, went on the offensive yesterday in Mosul, Iraq’s third largest city, after guerrilla attacks launched against police stations and bridges across the Tigris river in an apparent bid to relieve pressure on their trapped allies in Fallujah.

An American official acknowledged it might take “some time” to secure the city, 220 miles to the north.

Elsewhere, a series of attacks throughout central Iraq underscored the nation’s perilous security. In Baghdad, a car bomb exploded yesterday moments after an American patrol passed on Saadoun Street, killing 17 bystanders and wounding 30. There were no American casualties.

Another car bomb exploded in Kirkuk as the governor’s convoy was passing by, killing a bystander and wounding 14 people. Three Iraqis were killed in a shootout between American troops and insurgents in Samarra. Two car bombs injured eight people in Hillah.

Al Jazeera TV aired a videotape showing what the station said was an American contractor of Lebanese origin held hostage in Iraq. The balding, middle-aged man, who carried an American passport and an identification card in the name of Dean Sadek, was shown sitting in front of a green wall. Al Jazeera did not air any audio but quoted Mr. Sadek as saying all businesses should stop cooperating with American authorities.

The four-day Fallujah offensive has wounded an additional 178 Americans along with 34 Iraqi soldiers, the military said.

As night fell, U.S. Army soldiers and Marines attacked south of the main east-west highway that bisects Fallujah, a Sunni Muslim insurgent stronghold 40 miles west of Baghdad.

An Iraqi journalist in the city reported seeing burned American vehicles and bodies in the street, with more buried under the wreckage. He said two men trying to move a corpse were shot down by a sniper.

Two of the three small clinics in the city have been bombed, and in one case, medical staff and patients were killed, he said. An American tank was positioned beside the third clinic, and residents were afraid to go there, he said.

“People are afraid of even looking out the window because of snipers,” he said, asking that he not be named for his own safety. “The Americans are shooting anything that moves.”

Many, if not most, of Fallujah’s 200,000 to 300,000 residents fled the city before the assault. It is impossible to determine how many civilians who were not actively fighting the Americans or assisting the insurgents may have been killed.

Commanders said 1,200 to 3,000 fighters were believed to be in Fallujah before the offensive.

Most of the insurgents still fighting in Fallujah are believed to have fallen back to southern districts ahead of the advancing American and Iraqi forces, although fierce clashes were reported in the west of the city around the public market.

American officers said the majority of the insurgent mortar and machinegun fire yesterday was directed at American military units forming a cordon around the city to prevent guerrillas from slipping away.

Officers said that suggested that the insurgents were trying to break out of Fallujah rather than defend it.

Meanwhile, two Marine Super Cobra attack helicopters were hit by ground fire and forced to land in separate incidents near Fallujah, the military said. The four pilots were rescued, though one suffered slight injuries.

At an American camp outside Fallujah, Major General Richard Natonski, commander of the 1st Marine Division, said the operation was running “ahead of schedule,” but he would not predict how many days of fighting lay ahead.

He said troops had found an arms cache in “almost every single mosque in Fallujah.”

Mr. Natonski also said he had visited a “slaughterhouse” in the northern Jolan neighborhood, where hostages were held and possibly killed by militants. He described a small room with no windows and just one door. He said he saw two thin mattresses, straw mats covered in blood, and a wheelchair that apparently was used to transport captives.

Also, a Fox News reporter embedded with India Company of the 3rd Battalion, 5th Marine Regiment, said the unit found five bodies in a locked house in northwest Fallujah on Wednesday. All the victims were shot in the back of the head. Their identities were not known, although there were indications they were civilians, the report said.

American officials believe that the Al Qaeda linked terror movement of Abu Musab al-Zarqawi, who claimed responsibility for many of the kidnappings and beheadings of foreign hostages, used Fallujah as a base. They said they believe that Mr. al-Zarqawi may have slipped away before the offensive.

Last April, Fallujah militants fought Marines to a standstill during a three-week siege, which the Bush administration called off amid public criticism over civilian casualties.

The current offensive was begun so the government can hold national elections in January, although Sunni clerics have called a boycott to protest the Fallujah operation.

This offensive has gone swiftly, in part because of a larger ground force and massive use of air and artillery.

“Our air superiority is incredible,” said Sergeant Michael Carmody, 26, of Thompson, Pa., with the 3rd Battalion, 5th Marines in northern Fallujah. “All we can do now is clear through the city and look for survivors. Air power is our best friend.”

Military officials cautioned that the figure of 600 insurgents killed in Fallujah was only a rough estimate, and that many died in air and artillery bombardments ahead of the ground advance.

The chairman of the Joint Chiefs of Staff, General Richard Myers, said yesterday that “hundreds and hundreds of insurgents” have been killed and captured. He called the Fallujah offensive “very, very successful” but said it would not spell the end of the insurgency.

“If anybody thinks that Fallujah is going to be the end of the insurgency in Iraq, that was never the objective, never our intention, and even never our hope,” General Myers told NBC.

The attacks in Mosul may have been intended to divert attention from Fallujah. An American military spokeswoman, Captain Angela Bowman, said it could take “some time until we fully secure the city.”

Smoke rose over Mosul yesterday as American warplanes streaked overhead. City officials warned residents to stay away from the five major bridges. Militants brandishing rocket-propelled grenades were in front of the Ibn Al-Atheer hospital.