Tensions have been high in
US soldiers in an armoured vehicle reportedly fired on a group of Iraqis who attacked them with rocket-propelled grenades.
American troops fired randomly in all directions, injuring at least one civilian in the leg, said Aljazeera correspondent Tayseer Allouni.
AFP quoted US officials as saying American soldiers came under fire in two separate incidents in the city but none were injured.
Wednesday night’s clashes raised tensions in Fallujah. Residents said they had heard several explosions in the centre of the city, some 50 kilometres northwest of Baghdad.
Launchers from anti-tank grenades still lay at the scene of the latest clashes on Thursday and several shops had been destroyed.
According to residents, US occupation troops stormed homes in search of the attackers and further stepped up patrols across the city.
US tanks smashed two civilian cars. Passengers in one vehicle managed to escape but two civilians in a truck were killed, Aljazeera reported.
One Iraqi described the US response. “They went crazy, they fired everywhere,” he said.
Abdullah Khalaf Ahmad, a doctor at Fallujah Hospital, said wounds on the two victims indicated they had been shot by machine-gun fire.
Residents said the soldiers had prevented an ambulance from approaching the scene and a US armoured vehicle had smashed the pickup truck.
US troops denied they rammed into the truck before shooting dead the two Iraqis.
One of the victims was 19-year-old Hady Jaber, who residents said was to be married this week.
Some residents told Aljazeera the attackers were not from Fallujah and were trying to cause unrest in the city.
Fallujah has been tense since last month when US troops opened fire on Iraqi demonstrators, killing at least 16.
Iraqis have increasingly demanded a withdrawal of US occupation forces from their country since US tanks rolled into the heart of Baghdad on 9 April spelling an end to the Baathist government.
The situation was quiet on Thursday as residents complained about the presence of US occupation troops.
Iyad Qubaisi said, “Saddam never ruined our shops. Is this the liberation Bush talks about?”
Meanwhile, US administrator Paul Bremer ordered about 200,000 Baath party members to turn themselves over to US forces on Thursday.
Bremer has reportedly barred the top four ranks of the Baath party - about 35,000 people - from government jobs, reversing the policy of his predecessor Jay Garner of working with some senior Baathists.
But in recent days ordinary Iraqis say Bremer has not done enough to remove Baathists from top positions.
Iraqi hospital officials said dozens of former Baathists have been killed in the past three to four weeks, as Iraqis take revenge on members of the regime.
Under Saddam Hussein it was almost impossible to move up in any profession without being a Baath member.