US helicopters continue to circle over the restive city, reported Aljazeera's correspondent in Falluja Abd al-Adhim Muhammad on Thursday.
Earlier, US jet fighters and helicopters swooped low over the city, which has consistently resisted the occupation, and opened fire at various intersections.
Aljazeera's correspondent had said US armoured vehicles were moving into parts of the city, backed by air support.
The US military also confirmed that one of its Cobra helicopters was brought down outside of Falluja but said there were no casualties.
Resistance fighters fired rocket-propelled grenades and machine guns at occupation forces patrolling the main routes into the city centre.
US forces withdrew from Falluja
in May after weeks of fighting
Iraqi defence officials said members of the US-created Iraqi army fought alongside the resistance.
Correspondent Muhammad said a US convoy came under attack, destroying a Humvee armoured vehicle but causing no casualties.
Residents of the city, which witnessed a crippling siege in April, began to flee, reported witnesses.
A fragile truce was brokered in Falluja between the resistance and occupation after some of the deadliest battles broke out in April, leaving hundreds of Iraqi civilians dead.
The April battles prompted outrage in the Middle East and saw Iraqis from across the occupied country rallying to send medical supplies and food to the small city, some 50km west of Baghdad.
Last week the relative calm came to an end after a US air strike hit a civilian home, leaving 22 civilians dead.
The US-appointed Falluja Brigades, responsible for patrolling the city and maintaining calm, said many of those killed were women and children.
They also denied US claims that supporters of Abu Musab al-Zarqawi, who Washington describes as the head of al-Qaida in Iraq, were hiding in the house.