The UN's refugee agency estimates that about 8,500 Falluja residents have returned to their homes since the US bombardment ended two months ago.
US and Iraqi troops are checking every vehicle returning to Falluja
UNHCR officials said 85,000 inhabitants had arrived to inspect the damage and that around 10% of them had remained.
Whole families are said to have returned, with residents allowed to move back to half of 18 districts.
Others are said to be waiting for security to improve or for amenities to be restored.
"Until the elections take place and until they see what happens, they won't go back because they're scared," said UNHCR High Commissioner Marie-Helene Verney. "It's still pretty recent."
Falluja's population was about 250,000 before the attack and heavy bombardment to uproot insurgents from what had become a resistance stronghold.
"Many [returnees] said they intend to stay in their current locations until after the elections at the end of January," the UNHCR said in a statement.
In addition, it said that a number of those displaced have purchased property outside of the city.
"This may suggest that some [residents] are considering settling out of Falluja for an extended period," the agency said.
Many buildings were destroyed in the offensive. Electricity remains sporadic and municipal water is available only a few hours a day.
The main hospital is outside areas open to residents, meaning they have to pass through checkpoints to reach it, said UN officials.