Aljazeera's correspondent reported that for the first time in days most of Falluja's streets were crowded with people who raised the Iraqi flag and were clearly elated at being allowed to return.
The city's eastern gate, where the last checkpoint is still set up, was also crowded with people.
This reportedly follows a promise made by the new Iraqi commander of the city Major General Jasim Muhammad Salih to increase the number of families allowed to return.
Salih, who once served in Saddam Hussein's Republican Guard arrived, wearing his old uniform, to the cheers of bystanders in Falluja on Friday.
US occupation forces besieging Falluja for the past month turned to the former general in Saddam Hussein's army to lead a force to restore order in the city, 50km west of Baghdad and in the heart of what US forces have dubbed the Sunni Triangle.
The area has been a centre of resistance attacks on the US-led occupation of Iraq. More than 600 Iraqis were killed in the siege of the town.
US troops staying
Meanwhile, US marine commanders insist they still remain in control and can move back into the city at any time.
Hundreds of Iraqis have been
killed and homes destroyed
Amid questions as to whether the newly formed Falluja Brigade can be trusted, the commanders stress they will be closely monitoring the performance of the still incomplete Iraqi force, which is made up mainly of people who served in ousted president Saddam Hussein's former army.
They also say that while they are happy to put an Iraqi face on security operations in the flashpoint city, the Iraqi troops fall under their overall command.
Senior marine officers have been careful to avoid presenting the move as a withrawal from Falluja, where they lost dozens of men after laying siege to the city on 5 April.
But since the decision to send in the new force, marines have given up their main foothold in the city and pulled back to camps further away. They still have some positions on the outskirts of the city, but are expecting to move out of those within days.
US troops killed
Even as the deal was being implemented, fighting has continued in and around the city.
Two US occupation soldiers assigned to the Marine Expeditionary Force were killed in Al-Anbar province, which includes the flashpoint city, in a clash with resistance fighters.
The deaths follow the killings on Friday of two marines by an apparent car bomber near their base outside Falluja.
US marines will keep watch
over Falluja from its outskirts
Early on Saturday, bursts of gunfire ripped through the city as resistance fighters and US occupation forces skirmished intermittently despite a deal to hand security responsibilities back to Iraqis.
Sporadic gunfire continued overnight according to Captain Christopher Logan, a spokesman at the US marines base just outside the city.
Elsewhere in Iraq, at least one foreign security man was killed after a bomb exploded in the northern city of Mosul, local police said.
Three other foreigners and three Iraqis were wounded in the same incident.
The roadside bomb blew up as a convoy of five sports utility vehicles, typically used by the US-led occupation, sped through the city, 370km north of Baghdad, according to policeman Mahir Muhammad Amin.
And an Iraqi man was killed by US random fire in Heet city west of Ramadi, Aljazeera's correspondent reported.
The incident came after a US military vehicle was destroyed in an RPG attack.