The attacks on Friday focused on the eastern part of Falluja and at least five large explosions were heard, shaking the city and lighting up the night sky, they said. There was no immediate word on casualties and no further details.
Elsewhere violence flared across Iraq. Two children were killed and four of their siblings wounded when mortar rounds crashed on to their house overnight in a town north-east of Baghdad, a relative said on Friday.
"The mortar shells fell on their house, killing two children aged three and 12 and injuring four of their brothers and sister," said Hamad Ibrahim, a cousin who lives in the same house.
The target was probably a nearby police station in Muqdadiya, 100km from the capital, he said.
In an earlier attack by anti-US fighters, 17 Iraqis were killed on Sunday when two mortar rounds, apparently aimed at a US army base, slammed into a hostel used by factory workers in the northern town of Tikrit.
Former commander killed
In another incident, a former military commander in the army of ousted president Saddam Hussein was gunned down in the northern city of Mosul, police and medics said.
Colonel Faris Sheet died instantly after being hit in the head and chest at about 3.30pm (1230GMT), the sources said.
Mosul, the capital of Iraq's north, has seen a rash of car bombings and assassinations in recent weeks targeting US and Iraqi forces as well as local officials.
Mosul has seen frequent
assassinations in recent weeks
Meanwhile, an Iraqi truck driver was found shot several times in the head and chest near Balad, 75km north of Baghdad, police Colonel Jumaa Muhammad said.
The driver, identified as Muhammad Jabbar Karim, worked for a company that "had probably cooperated with the American army," the colonel said.
This was the tenth Iraqi driver in a month found killed in this Sunni Muslim area.
Contractor found dead
An Iraqi contractor working with US forces was also found shot to death on Friday in the town of Balad, police Lieutenant Colonel Hamad Ahmad said.
The victim, Adil Muhammad al-Kim, was kidnapped from his home three days ago by unknown men, Ahmad said.
Also, an American soldier was been killed and five others were wounded in an attack on a military base near Falluja.
The latest death brings to 1122 the number of US military personnel killed since the US-led war on Iraq was launched in March 2003, according to Pentagon figures.