Witnesses quoted by AFP said on Thursday that the convoy had stopped when one of its vehicles broke down in the town of Khaldiyah, 30km west of Fallujah.
Gunfire and mortar fire were exchanged for more than an hour, after masked men attacked with rockets.
The same witnesses reported seeing American soldiers severely wounded but there was no official confirmation.
However, there was an unusual calm in Najaf. Armed Shia militiamen disappeared from the Iraqi city after US forces declared their intention to crack down on the public brandishing of weapons.
Only policemen with armbands and shrine protection forces were seen carrying weapons in the centre of the city 180km south of Baghdad on Thursday.
Even followers of anti-US occupation Shia cleric Muqtada Sadr put their arms away and guarded his home in civilian clothes.
Shia cleric Muqtada al-Sadr - one
of the most outspoken voices
Najaf governor Haidar Mahdi Mattar al-Mayali has been mediating between US forces and Muqtada Sadr, who had refused to see his militia carrying US permits.
"We do not want to carry arms on the strength of permits issued by the occupation forces. We are in talks with the governor to have permits stamped by Najaf authorities," said Sadr's spokesman.
Aljazeera team released
Meanwhile, occupation forces may investigate the detention of two reporters from Aljazeera, according to US Commander Ricardo Sanchez on Thursday – who insisted their arrests were justified.
Asked by an Aljazeera correspondent whether the arrests - the eighth involving the television's journalists here since the war - amounted to "harassment", Sanchez said: "There is an investigation ongoing."
One reporter, Atwar Bahjat, was released after spending the night in a US military holding camp at Baghdad airport.
The television said she had been detained while covering a bomb attack in the al-Ghazzaliyah district of the capital.