It was unclear what caused the clashes, but marines officers said that both sides had suffered casualties.
The US military announced that three US marines had been killed in al-Anbar province while conducting security operations.
"We did have three marines killed in action in 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 fighters on marines in the town's northern districts. Falluja is one of the largest towns in the vast western province of al-Anbar.
Witnesses said US F-18 fighter-bombers struck at targets in the town's southern neighbourhoods. 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 town, were supposed to return to their homes.
Still not secure
Iraqi journalist Fadil al-Badrani told Aljazeera Fallujan families started entering the town early in the morning from its northwestern and eastern gates.
The sound of explosions deterred
many Fallujans from returning
"Some families entered the town in their cars after being searched, heading towards the Andalus neighbourhood west of the town, at the eastern side of the Euphrates," he said.
The BBC reported that residents who had planned on returning to the war-ravaged town turned back after they heard explosions rock the town 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 town. I just want to see if my house has been damaged," said Muhammad Abud, 45, queuing on the edge of the town.
"I don't want to come back yet. I've heard it's still not secure."
No other choice
But most Fallujans felt they had no other choice but to brave the insecurity and return to their homes.
Speaking to Aljazeera from the outskirts of Falluja's Andalus entrance, Abd Allah Mahmud al-Isawi, said: "Displaced families gathered at the entrances to enter the town, not because they like coming back to their demolished homes but escaping from the cold weather, hunger, shortage of water, food and services they have been suffering from."
He said they had suffered in the makeshift tents, structures, schools, and government buildings in the vicinity of the town, where they were forced to stay for the past six weeks.
Al-Isawi also said US soldiers had distributed printed instructions which returning residents had to abide by while in the battered town.
"The instructions stipulated that no car can move inside the city. No child or elderly can cross the street and they are not responsible for anyone's security, meaning that residents will live in a cage inside the town."
According to another Falluja resident, who returned to the town for the first time since 8 November, charred and half-eaten corpses littered the streets.
Many Fallujans returned to find
decaying bodies in their homes
"We headed to the area where we live and saw some bodies lying about the streets," Abd al-Rahman Salim said.
"I entered my neighbour's house and found him, after identifying him from an identity card. His body was lying on the ground, nothing left of him but some bones.
"The scene was very shocking and I could not stay as the smell in the houses and the street was intolerable," he said explaining why he left Falluja.
"Before entering the city, they [US forces] told us that the town is suitable for living but we were shocked when we found no water, no electricity and no simple services."