"We have received three dead", Dr Ali Hayad said.
The latest raids targeted the districts of Julan and al-Askari. Falluja has been sealed off by US and Iraqi troops since Thursday.
The US army in a statement confirmed a raid "against an armed al-Zarqawi terrorist checkpoint in the Julan district of the city of Falluja" around 10.45pm (1945 GMT).
"The terrorists operating this illegal checkpoint were heavily armed and were using the blockade to disrupt traffic, intimidate and harass local citizens, and interrogate and detain local civilians," the statement added.
Reporters quoted witnesses as saying tanks could also be seen moving on a highway just outside Falluja and were shelling the city.
Iraq's US-backed interim government, headed by interim Prime Minister Iyad Allawi, has warned that it will launch a major offensive in Falluja if the city does not hand over alleged al-Qaida linked Jordanian Abu Musab al-Zarqawi.
Scores of houses in Falluja have
been levelled by US air strikes
Falluja representatives and fighters in the city say they have seen no evidence of al-Zarqawi being there.
US warplanes bomb rebel targets in Falluja on a near daily basis, claiming they are delivering "precision strikes" against al-Zarqawi's alleged network.
Residents say the strikes kill civilians.