Colonel Steve Warren said more than 20 strikes have been carried out in the past four days, destroying IS positions.
The raids are in support of Iraqi forces who are trying to retake Falluja from IS.
Meanwhile there are dire warnings about conditions in the city.
The IS commander in the city, Maher Al-Bilawi, was killed in bombardments targeting IS fighter positions and gun emplacements, Col Warren said.
However, the colonel warned that it was unclear how long the battle to retake the city would last.
Islamic State: The full story
Some 50,000 civilians remain trapped in the city and have been told via leaflet drops to avoid IS areas and put white sheets on their roofs, Col Warren said.
The UN says it has reports of people dying of starvation and being killed for refusing to fight for IS.
"We have dramatic reports of the increase of the number of executions of men and older boys, refusing to fight on behalf of Isil," said Melissa Fleming, a spokeswoman for the UN High Commissioner for Refugees, using an alternative acronym for IS.
"Other reports say a number of people attempting to depart have been executed, or whipped. One man's leg was amputated reportedly."
The UN says hundreds of families were able to flee the city on Friday with the help of government forces.
The assault is being carried out by a combined force comprising thousands of Iraqi army troops, the federal police and Sunni tribal fighters, Col Warren said.
Militia forces were also involved but had pledged to remain outside the city, he added.
Falluja fell to IS in 2014, a key moment in its rise that saw it declare a caliphate across swathes of Iraq and Syria.

The report, a summary of which was released by the Homeland Security Department, said the agency needed more plainclothes and uniformed staff.
It added that the White House needed a new, taller fence.
The review came after an intruder with a knife entered the building.
Omar Gonzalez, a former US soldier, was apprehended deep inside the presidential residence in September after he had scaled a fence around the building and evaded several guards - including one with an attack dog.
Julia Pierson, the Secret Service director at the time, resigned partly as a result of this breach.
The Secret Service is tasked with guarding the US president, as well as several senior government officials.
According to an executive summary of the independent review, the agency's next director "will have to make difficult choices, identifying clear priorities for the organisation and holding management accountable for any failure to achieve those priorities".
"Only a director from outside the [Secret] Service, removed from organisational traditions and personal relationships, will be able to do the honest top-to-bottom reassessment this will require."
The review also said a better fence should be built "as soon as possible", recommending one that was several feet higher and curved outwards, making it harder to scale.
However, the review noted that the problems in the agency "go deeper than a new fence can fix". The panel said the agency's staff were over-stretched, working "an unsustainable number of hours".
It called for boosting the service's ranks by 85 special agents and 200 uniformed officers, to reduce overtime and allow staff to receive regular training.
The four-member panel based its findings on interviews with 50 employees of the Secret Service. The panel admitted that many of its recommendations had been made before - but not implemented.
Many details have already emerged of the security lapses that allowed Mr Gonzalez to enter the White House, pointing to a lack of training, bad staffing decisions and failures in communication.
Mr Obama and his family were not at the White House when the intrusion happened, having departed about 10 minutes earlier by helicopter.
Mr Gonzalez has been indicted on charges including unlawfully entering a restricted building or grounds while carrying a deadly or dangerous weapon and unlawful possession of ammunition.
The intrusion came after a series of embarrassing lapses by the Secret Service - including reports that agents had used prostitutes while on duty in Colombia.
The Islamic State group's commander in the besieged Iraqi city of Falluja is among 70 militants killed in coalition air strikes, the US military says.
[NEXT_CONCEPT]
The US Secret Service, which guards the US president, is too insular and must recruit its next head externally, a review prompted by a White House security breach says.