Commanders are also concerned about what one senior military officer described as the "Fallujah effect," with insurgents throughout the country launching attacks in support of those who remain in the city.
In Ramadi, hundreds of armed militants flooded the streets, as U.S. helicopters kept watch over head. In Baquba, an Iraq police station was ambushed, killing one officer and wounding eight others.
In Baghdad, car bombs hit an Iraqi police checkpoint at a hospital, as well as two churches. Further north in Kirkuk, another car bomb exploded, and two U.S. soldiers were killed in mortar attacks in Mosul.
The continued violence means that even if the battle of Fallujah is successful, the problems will not be over.
"We don't know how many people can go underground, simply go back into the population, or how many can escape what is a loose surrounding force around the city," said military analyst Tony Cordesman, an ABC News consultant. "We have to understand this is a battle. It is not a war."
There are still concerns that the insurgents are regrouping inside Fallujah for a final assault.
ABC News' Martha Raddatz filed this report for World News Tonight.
