Earlier, eight US marines were killed in two separate incidents in Iraq's al-Anbar province, the military said, a day after American warplanes pounded Falluja with missiles.
It was unknown if the deaths were connected to the fighting in the volatile western Iraqi city.
In a statement, the military said the eight marines with the 1st Marine Expeditionary Force died while conducting security and stabilisation operations in al-Anbar province, a vast region that comprises Falluja and Ramadi.
The statement gave no other details about the deaths, saying the release of more information could place US personnel at risk.
The latest deaths raise to 1296 the number of US military personnel killed in Iraq since March 2003.
On the clashes in Falluja, spokesman Lieutenant Lyle Gilbert said: "The strikes were conducted throughout the day and were called in by troops in (armed) contact with and observing the enemy moving from house to house."
Falluja resident Abd Allah Ahmad is quoted as saying the fighting began after US soldiers brought 700 to 800 men into the city to clear rubble from damage caused by November's offensive.
A US tank was slightly damaged
in an attack in Tikrit
"The clashes started as soon as the young men entered the city," Ahmad said.
"The American troops were surprised and decided to launch military operations."
Elsewhere, two anti-American fighters died after detonating their explosives-packed car alongside a US tank in Tikrit, north of Baghdad, at about 10.45am (0745 GMT) on Monday, military spokesman Staff Sergeant Robert Powell said.
No soldiers were wounded and the tank sustained minor damage.
Four decapitated bodies in civilian clothes were found south of Baghdad and their identities were unclear, police said. The victims, believed to be Iraqis, were found in Haswa, about 40km south of the capital.