The force of the blast on a dusty stretch of wasteland nine miles north of Fallujah, a hotbed of Sunni insurgents, wrecked two Humvee vehicles and hurled the suicide car's engine a "good distance" from the site, witnesses and military officials said.
Early Tuesday, residents reported strong explosions around the city. The U.S. command in Baghdad said it had no information on what was going on.
Meanwhile, three other U.S. soldiers were also wounded in a roadside bombing in eastern Baghdad.
In other developments
After the Fallujah attack, medical teams in helicopters ferried away the injured from the blazing wreckage and troops sealed off the area.
Fallujah hospital officials said four Iraqis were wounded by gunfire from U.S. troops near the site of the bombing, but the U.S. military had no confirmation.
The military condemned the bombing as "a desperate act of inhumanity" but insisted American troops will stay the course in Iraq until local forces are in a position to take over security operations.
Hours after the attack, an unmanned U.S. spy plane crashed in Fallujah. Afterward, jubilant residents picked up pieces of debris and danced in the streets, displaying pieces of the aircraft to reporters, witnesses said.
The bombing underscored the challenges U.S. commanders face in securing Fallujah and surrounding Anbar province, the heartland of a Sunni Muslim insurgency bent on driving coalition forces from the country.
"The duty of bringing security to the Anbar province is inherently dangerous," the military said in the statement.
U.S. forces have not patrolled inside Fallujah since April, when U.S. Marines ended a three-week siege that left hundreds dead. Fallujah has since fallen into the hands of insurgents who have used it as a base to manufacture car bombs and launch attacks on U.S. and Iraqi government forces.
The U.S. withdrawal left behind a population now living under the iron-fisted rule of Islamic fundamentalists, reports CBS News Correspondent Barry Petersen. They have created what some call a Taliban-like society, where crimes are punished by beheadings and working with Americans is a death sentence.
"It is certainly a no-go area for the authorities in Iraq and it's been a no-go area since the fall of Saddam," said Michael Clarke, an Iraq expert and professor at King's College in London.
Fallujah is rapidly becoming a high-profile litmus test of American power. A major assault is being planned to pacify the city in time for Iraq's elections early next year.
The Marines killed were members of the 1st Marine Expeditionary Force. Names of the dead U.S. and Iraqi troops were withheld pending family notification.
The Fallujah attack resulted in the largest number of Americans killed in combat in a single day since May 2, when nine U.S. troops died in separate mortar attacks and roadside bombings in Baghdad, Ramadi and Kirkuk.
On Sunday, both Iraqi Minister of State Qassim Dawoud and a Defense Ministry spokesman publicly proclaimed al-Douri's capture. Later in the day, Defense Minister Hazem Shaalan said word of his arrest was "baseless."
The reports on al-Douri — the most wanted Saddam-era henchman still at large — came as an embarrassment to interim Prime Minister Ayad Allawi's government and exposed a lack of coordination among ministers competing for influence ahead of January elections.
Al-Douri was once the vice chairman of the Baath Party's Revolutionary Command Council and U.S. military officials believe he played an organizing role in the 16-month-old insurgency.
Ministry spokesman Sabah Kadhim said unspecified tests had shown that a man being held in Iraqi custody was actually a relative of al-Douri who had played only a minor role in Saddam's regime but was nevertheless wanted by authorities.