U.S. and Iraqi forces fanned out across a vast region south of Baghdad early Tuesday in what U.S. commanders described as a major operation to regain control of lawless areas where insurgents routinely use supply routes to bring weapons and fighters into the capital.

More than 3,000 troops will target dozens of insurgents in raids extending west of the Euphrates River, military officers said. On Tuesday, U.S. troops took control of a bridge that insurgents had used to move bombs, money and people into Baghdad, sowing the growing disorder there, U.S. military officials said.

Three U.S. Marines were wounded in an ambush near the marketplace in the city of Haswah, about 50 miles south of Baghdad, just before the operation began. Another Marine and two Iraqi National Guardsmen were injured by a car bombing Monday morning about 20 miles away near the city of Latifiyah, U.S. military officials said.

The operation here is part of a U.S. strategy to reclaim regions in Iraq that have fallen into the hands of insurgents. Last week, U.S. and Iraqi forces regained control over Samarra, north of Baghdad, in what U.S. officials described as a template for dealing with problem areas before planned nationwide elections in January. Fallujah, Ramadi and Baghdad's Sadr City neighborhood are among the key areas still effectively controlled by the insurgency.

"Right now, time is not on their side," said Col. Ron Johnson, commander of the 24th Marine Expeditionary Unit, which is conducting much of the operation here. "If we can get to the elections, they know we'll get the upper hand. The next three or four months are going to be the high-water mark" for military activity.

Iraq's interim president, Ghazi Yawar, said Tuesday that his government was trying to avoid storming Fallujah, which has been controlled by insurgents since April, when the Marines pulled out.

"We are trying to work out a way for Iraqi forces to enter the city peacefully and take control. We are trying to have coalition forces remain outside the city as support forces," Yawar told al-Arabiya television.

"I told people in Fallujah that this will not be a picnic, this will be very hard and decisive. We do not want our people to be hurt," Yawar said.

In scattered violence Tuesday, a car bomb exploded near a U.S. convoy in Ramadi, west of Baghdad, killing four Iraqis and wounding two, according to hospital officials. The U.S. military said in a statement that another car bomb, in the northern city of Mosul, killed three civilians and wounded four foreign troops, and mortar fire killed one civilian and wounded another in Baghdad. Meanwhile, five decapitated bodies, all believed to be Iraqis, have been found in northern towns, local officials said.

In the military operation unfolding south of Baghdad, U.S. commanders said they were seeking to gain some measure of control over an area encompassing roughly 600 square miles, stretching southwest to Karbala and due south to Hilla. Although not as notorious as some other insurgent strongholds, the region is hostile and dangerous, U.S. Marines say. The 1st Battalion, 2nd Marine Regiment has suffered two deaths and 100 wounded since its arrival July 18 at Camp Iskandariyah, a forward operating base on the Euphrates River.

About 40 mortar rounds were fired into the base the day the battalion arrived, according to its operations officer, Maj. Matt Sasse, who said he was nearly hit. Sasse said the battalion is routinely pummeled by roadside bombs and small-arms fire.

"There's so much going on here," he said. "It makes my head hurt."

Operation Phantom Fury, which began with two pre-dawn raids against suspected insurgents in the city of Musayyib, is designed "to kill the enemy and disrupt his activities" and "show him that he can't do whatever he wants," Sasse said.

The operation's centerpiece is the seizure of the Jurf al-Sakhr Bridge, which connects the towns of Latifiyah -- where two senior Iraqi customs officials were assassinated Monday -- and Nayif al-Ajil. The bridge is a key crossing point on the Euphrates south of Baghdad, and U.S. officials say they believe followers of the Jordanian-born militant Abu Musab Zarqawi use it to supply the insurgency in the capital. Zarqawi and other insurgent leaders have operated with impunity west of the Euphrates, according to military sources.

About 600 U.S. soldiers, transported by Stryker armored assault vehicles, took the bridge Tuesday morning without resistance, according to U.S. officials. They declined to comment on how long U.S. forces would maintain control over the bridge.

In Musayyib, Marines, accompanied by dozens of Iraqi Special Forces troops who rode on a flatbed truck, executed what U.S. commanders described as the first of what will be dozens of targeted raids across the region.

A Muslim cleric, suspected of giving haven to insurgents and inciting violence against the American presence, was detained, and dozens of cassette tapes and literature were confiscated.

But the second raid appeared to show the challenges of searching for suspects who can easily melt into their communities. At approximately 3 a.m., Marines provided support for dozens of Iraqi Special Forces troops who used a battering ram to storm a three-story house in Musayyib in search of a man described as an insurgent leader.

Inside, they found the man's sister and his 18-year-old nephew, who identified himself as Abdullah. U.S. and Iraqi forces ransacked the house but found no weapons. Abdullah, blindfolded and bound, was taken away in the truck while his mother's piercing cries echoed down the empty street at 4 a.m.

"He's not in trouble. It's okay -- we just want to ask him a few questions," said one Marine, trying to console the woman. After accusing the Iraqis of stealing her money during the search, she slumped against a wall, sobbing, as the vehicles drove away with her son, who said he was a high school student.

Abdullah told a U.S. interrogator that his uncle had a house on the other side of the river and offered to take the U.S. and Iraqi forces there. The convoy wound past a market that was just opening and came to a quiet neighborhood overrun by stray dogs.

Again the U.S.-supported Iraqi forces bashed in the door, but they found this house empty except for random items: boxes for radios and bug zappers and a clock that had not been reset since daylight saving time in Iraq ended Friday.

"Did you know this house was vacant?" a Marine asked Abdullah.

"He was here three days ago," the teenager replied.

"That's a lie," the Marine muttered.

The raid ended at 4:30 a.m., as the muezzin's call to prayer echoed through the streets.

"You look disappointed," one officer said to another.

"I am," said the other officer.

"At least you're going back alive," said the first.

Children gather around a charred vehicle after a car bombing in the northern Iraqi city of Mosul. Three civilians were killed and four soldiers were wounded. Interim President Yawar wants Iraqi forces to enter Fallujah peacefully.