Witnesses said US aircraft and tanks blasted at least two targets in the Golan district of the city, scene of many clashes over the past three weeks.
"I can hear more than 10 explosions a minute. Fires are lighting the night sky," one witness told Reuters. "The earth is shaking under my feet."
Mosques in the city blared with calls for citizens to take up arms to defend the city, the witnesses said.
Live television pictures showed two large fires some 150 metres (yards) apart. Thick smoke rose over the area. A US military spokeswoman said: "We don't comment on operations before they end."
The fighting came hours after a US deadline for insurgents in the city of 300,000 to hand over their weapons. US forces have laid siege to Falluja since April 5.
Hundreds of people have been killed in the city, long a centre of insurgency against the US-led occupation of Iraq.