The bombing of Falluja on Sunday took place after skirmishes between US forces and fighters in the eastern parts of the town.
An Iraqi journalist, Fadil al-Badrani, described the clashes as the fiercest in two weeks.
Columns of smoke have been seen rising from the areas of al-Askari, al-Shuhada, al-Sinai and al-Jubail, the journalist told Aljazeera.
Al-Badrani said explosions have also been heard in several areas of the city.
The Iraqi Red Crescent has been unable to enter the neighbourhoods to distribute medical and food supplies.
Al-Badrani said some dead bodies were still lying in the city's streets.
Meanwhile, a car bombing rocked Arbil on Sunday, a city in Iraq's relatively peaceful northern Kurdish region, wounding two people, witnesses said.
Sunday's attack was the first in the city since 105 people were killed in two attacks in February this year.
In other incidents, 10 Iraqi national guardsmen were killed and another two wounded when fighters attacked the bus they were travelling in through the Iraqi town of Hiyt, Aljazeera has learned.
Also, Iraqi police found seven bodies of African description near the Ain al-Asad base in the town of Haditha, west of Baghdad.
In areas around Baquba, US forces and Iraqi guardsmen carried out search operations and arrested about 75 people.
In Mosul, a military spokesman said heavy action took place after fighters opposed to the interim Iraqi government attacked a US military patrol that was trying to seize an arms dump on Saturday.
Fighters set off a car bomb, then
opened fire on US troops in Mosul
The fighters set off a car bomb and then opened fire with rifles, grenade launchers and mortars on the unit that moved on to the arms cache. Troops later destroyed the weapons.
There was an "unknown number of enemy casualties" and eight soldiers were slightly wounded, Lieutenant-Colonel Paul Hastings said.
There was no let-up in attacks on US forces on Sunday. A car bomb exploded near a US military convoy, wounding at least two passersby, witnesses and the US army said.
The bombing took place in al-Anbar province but caused no US casualties, a marines spokesman said.
The attack happened at about 10.30am (0730 GMT) on the road between Haditha and Rawah, about 250km northwest of Baghdad.
Senior officers killed
In other attacks across the country, three high-ranking Iraqi police officers and seven Iraqi national guardsmen were among those killed.
The guardsmen were shot dead in the town of Hiyt in western Iraq when armed men ambushed their minibus, Captain Ahmad Jasim of the US-backed Iraqi force said. Three others were wounded.
Seven guardsmen were killed in
an ambush in Hiyt in west Iraq
In southern Baghdad, fighters killed a police brigadier and a colonel, a police source said.
Near the northern town of al-Sharqat, a police colonel was one of two officers killed in an ambush.
Three others, including another colonel, were wounded.
A police source said the brigadier and colonel killed in Baghdad worked at the interior ministry.
In the centre of the northern oil capital of Kirkuk, a car bomb exploded, badly damaging a US Humvee patrol vehicle and wounding two soldiers and an interpreter, the US military said, adding that the wounded were in a stable condition.
Security officials and civil servants have become prime targets for fighters opposed to the US military presence and to Iraqis working for the US-backed authorities.
There are fears violence may increase before elections scheduled for 30 January.
In what will be a worrying sign for the interim government eager to pacify the country before the polls, the election infrastructure is already coming under attack.
A bomb damaged an office for election workers in the town of Zab, southwest of Kirkuk, wounding a civilian, police said.
In other violence, four employees of the education ministry were wounded when the bus taking them to work in Baghdad was sprayed with gunfire.
A civilian motorist was wounded on the main highway between Hilla and Karbala, south of the capital, when a roadside bomb went off, missing a convoy of guardsmen, police said.