US Defence Secretary Donald Rumsfeld said pockets of resistance remained, but US-led troops were now operating in much, if not all, of Falluja.
The first aid convoy has arrived, amid fears of a humanitarian crisis.
But a relief agency spokeswoman told the BBC that US forces had refused to let them distribute the supplies.
The fighting is not over yet. The insurgents are broken up and scattered in the city. Their command and control has been disrupted but they continue to fight in small pockets in the city.
More than 1,000 rebels have been killed and about 200 captured, National Security Minister Kasim Daoud said.
However, he said militant Abu Musab al-Zarqawi, whose group has claimed attacks across Iraq and a series of hostage beheadings, had escaped from the city.
The US-led assault on Falluja is aimed at taking back control from insurgents and stabilising the country before planned elections in January.
US forces say 22 Americans and five Iraqis have been killed, and almost 180 US soldiers wounded, since the assault began on Monday. More…
There is a sense that the process of stamping out these insurrections will be like playing “Whack-A-Mole !”. – zzb