Clashes have erupted between US marines and Falluja's fighters as displaced families were set to return to their homes in the battered city on Thursday.
It was unclear what caused the clashes, but marine officers said that both sides had suffered casualties.
The US military announced that three US marines had been killed in the Al-Anbar province while conducting security operations.
"We did have three marines killed in action in the Al-Anbar province today," spokesman Lyle Gilbert said. "They were conducting security and stabilisation operations."
He declined to provide further details or say whether the deaths were linked to an attack by Falluja resistance on marines in the city's northern districts. Falluja is one of the largest cities in the vast western province of Al-Anbar.
In the devastated city itself, witnesses said US F-18 fighter-bombers struck at targets in the city's southern neighborhoods. Tank and artillery fire were also heard.
The fighting erupted on the day the first 2000 residents, displaced by last month's bloody US-led offensive on the city, were supposed to return to their homes.
**Still not secure***
Iraqi journalist Fadhil al-Badrani told Aljazeera Fallujan families started entering the city early in the morning from its northwestern and eastern gates.
"Some families entered the city in their cars after being searched, heading towards the al-Andalus neighbourhood west of the city, at the eastern side of the Euphrates," he said.
The BBC reported that residents who had planned on returning to the war-ravaged city turned back after they heard explosions rock the city and saw plumes of smoke rise above buildings. Some said it would not be safe for them to remain.
"I don't want to stay in the city, I just want to see if my house has been damaged," said Muhammad Aboud, 45, queuing on the edge of the city.
"I don't want to come back yet. I've heard it's still not secure."
**PHOTO CAPTION***
A man argues with a US and Iraqi soldiers as he waits to be allowed to enter Fallujah on the city limits Thursday, Dec. 23, 2004. (AP)