The fighting in Falluja happened despite a ceasefire designed to end a violent standoff in the town, a US officer said.
"Eight people were killed and three vehicles destroyed," Lieutenant Colonel Brennan Byrne told reporters on Tuesday, adding that US occupation forces fired mortar rounds on fighters carrying rocket-propelled grenades.
In Baghdad, 21 people were killed and about a 100 wounded when fighters fired mortar rounds on a detention facility, a senior US occupation military spokesman said.
Deputy director Brigadier General Mark Kimmitt told a press conference in Baghdad on Tuesday that the rounds slammed into the Baghdad Confinement Facility administered by the US-led occupation forces.
The detention centre was in the
control of occupation forces
Initial reports indicated that all the casualties at the detention cerntre, or the Abu Ghraib jail, just west of Baghdad, were prisoners, but Kimmitt could not say if they were held as suspects for criminal or resistance activities.
In the northern Iraqi city of Mosul, five US troops and three Iraqi civilians were injured when a US convoy was targeted by two roadside bombs, according to occupation and Iraqi officials.
Two of the US soldiers were critically wounded in the attack at al-Islah al-Zirai, west of the city centre, 370 km north of Baghdad, at about 9:15 am (0515 GMT) on Tuesday.
"Two roadside bombs exploded at the same time. It was a very strong explosion injuring five soldiers, two of them are in a critical condition," said a US military spokesman.
Three US military Humvees were damaged in the blast, police said.
Three Iraqi civilians were also injured in the blast, according to Dr Musaab Hani at the Madinat al-tib hospital in Mosul. "They had operations to take out the shrapnel," he said.