The patrol, from the 82nd Airborne Division, was first hit by an exploding homemade bomb, and then by small-arms fire, the military said. American troops then raided a nearby mosque in an apparent search for the attackers and detained three Iraqis.
It could not be learned immediately whether there were any Iraqi casualties, although two civilian trucks were damaged in the action, including one left dangling on a bridge, apparently from what witnesses said was a rocket-propelled grenade strike.
The attack occurred about 20 yards from the main bridge leading into Fallujah from Baghdad, 35 miles to the east, when about 30 soldiers on foot, accompanied by five Humvees, were on patrol along the highway.
This was the same general area where a U.S. Army ammunition truck, part of a convoy, broke down on the main road Sunday and came under attack. That truck and possibly two other vehicles apparently were hit by rocket-propelled grenades. Dozens of Iraqi youths danced and cheered as the vehicles went up in flames.
It was one of 43 attacks on Americans all over Iraq on Monday, reports CBS News Correspondent Kimberly Dozier.
The soldier killed Monday was the 339th American to die in Iraq, the 218th to perish in combat. Since May 1, when President Bush declared an end to major combat, 104 U.S. soldiers have been killed by hostile action.
In other developments:
U.S. Central Command reported 15 attacks on forces of the U.S.-led coalition in the 24 hours that ended at midday Sunday, down from a recent average of 22 a day.
Most occur in the so-called "Sunni Triangle," a Sunni Muslim-dominated area stretching from the west of Baghdad to the north. The area was a strong base of support for Saddam Hussein's Baath Party regime.
American officials blame the insurgency largely on die-hard Baathists, but many here believe other Iraqis resentful of the U.S. military presence have joined in the hit-run attacks.
In an opinion-page piece in Sunday's New York Times newspaper, Allawi, head of the 25-member Governing Council for October, said the decision by U.S. occupation officials to dissolve the 400,000-man Iraqi army after the war's end in April produced a "security vacuum that let criminals, die-hards of the former regime and international terrorists flourish."
It is "vital" to recall Iraqi army units now, six months after they disintegrated before the U.S.-British military advance, Allawi wrote.
The Bush administration is urging other nations to send troops and money to help the United States in Iraq. Washington hopes that last week's unanimous U.N. Security Council vote on a U.S.-sponsored resolution on Iraq will prompt nations to contribute.
"We'll take as much money as we can get," Secretary of State Colin Powell said ahead of a donors conference due to begin Thursday in Madrid.
"And I think the resolution will encourage some countries to give who might not have had a basis to give before the resolution was passed," he said on "Fox News Sunday."
The State Department study, a yearlong effort involving more than 200 Iraqi lawyers and business people as well as other experts, began in April 2002. It found more significant problems with Iraq's infrastructure than the Pentagon foresaw, and predicted Iraqis would be unenthusiastic about U.S. occupiers.
Officials told The Times that Pentagon official ignored the report until recently.
Iraq's most influential Shiite Muslim cleric warned of "new grave problems" if nothing is done to stem the proliferation of firearms in the country and blamed recent clashes between his supporters and followers of a radical cleric on the weakness of the central government.
Grand Ayatollah Ali Hussein al-Sistani also warned that there could be "no substitute" for a general election to choose delegates to a convention to draft a new constitution despite U.S. demands for a quicker selection process.