The military reported four marines killed, and two others were wounded. The occupation troops were killed by hostile fire on Monday, bringing to five the number of marines killed that day.
The military did not give details on the deaths, saying only that they took place in Anbar province, where Falluja is located.
Witnesses reported another American killed in fighting on Tuesday, but the report was not immediately confirmed.
The military also reported three US occupation soldiers killed in a single Baghdad neighborhood on Monday and on Tuesday.
The deaths bring to at least 614 the number of US occupation soldiers killed in Iraq since the war began.
US and Iraqi troops have sealed off the town for more than 24 hours, blocking roads and digging trenches. But the bulk of the force has remained on the city's edge.
American commanders have vowed to root out resistance fighters after the slaying last week of four American civilians.
The assault on Fallujah, west of Baghdad, comes as US officials are taking a more aggressive approach on another front: against a fiercely anti-American Shia leader, Muqtada al-Sadr, who has built up a private army, the al-Mahdi Army.
The only operating hospital in Falluja, about 65km west of Baghdad, was hit by US tank and missile fire overnight, reported Aljazeera's correspondent Ahmad Mansur on Tuesday.
Restrictions have brought the
town's transport to a standstill
A car carrying a corpse was still smouldering outside the private hospital. Its owner was driving to the hospital in the early hours of Tuesday when he came under US fire, reported Mansur.
Mansur reported on Monday that unconfirmed reports suggested that 20,000 US marines were besieging the town, trying to enter it from different points.
Aljazeera's correspondent in Falluja reported late on Monday several loud explosions across the mainly Sunni Muslim town, where US helicopters had been in action, firing a number of missiles.
Husayn Ali, a member of the Aljazeera production team in Falluja, was monitoring the tense situation on Monday.
"Falluja's main and minor entry points are totally closed," he said. "US forces are not allowing anyone in or out. We talked to US forces. They said they have orders to seal the city off for two or three days.
"We also visited the Golan district where clashes took place earlier today between fighters from Falluja and US forces," Ali said. "We saw signs of fierce confrontation. US forces have bombed the district. We saw several destroyed houses.
"Golan inhabitants say US forces used cluster bombs and missiles against them," he said. "Citizens of the city are completely enraged - but not afraid - waiting for the coming events," the correspondent said.
Mansur said US forces had issued printed statements to residents.
The leaflets outlawed demonstrations, the possession of firearms and imposed a 7pm to 6am daily curfew. Residents were advised that in the event of a raid by US forces, all family members should gather in a single room in the house.
US occupation forces have taken
heavy losses in Falluja
"This indicates that door-to-door operations will be launched by US forces," the correspondent had reported.
Aljazeera had also received a statement issued by a group in al-Anbar province calling itself the Jihad Brigades, urging followers of the Shia leader al-Sadr to continue resisting.
Aljazeera.net spoke by phone to a taxi driver in Falluja. Giving his name only as Muhammad, he said he was unable to work because the roads were closed and people had not gone to work.
"The Falluja economy is dependant for goods and services on the agricultural and industrial towns and cities in the region. Today, vegetables and food could not be brought into the town. People who work outside Falluja could not go to work," he said.
"Even Falluja's main hospital is inaccessible because it is located out of the city across the Euphrates river, and the bridge is closed. Today I saw an ambulance driver negotiating with US soldiers to let him cross the bridge. They let him through after a long and tiresome argument."
Falluja has no colleges and universities, so students from the town mostly study in Baghdad.
"Every morning I transport a number of students to Falluja's main bus stop. But today no students asked me to take them," said Muhammad.