President George W. Bush said in Washington yesterday that U.S. forces have made "substantial progress" toward securing the city.
And the man commanding the U.S. Marines there, Lieutenant General John Sattler, was similarly optimistic.
"The operation is going extremely well and we will continue to press the enemy until we have in fact returned Al-Fallujah to the Al-Fallujian people," Sattler said.
Sattler said U.S.-led forces are now in control of most of the city.
But he added that there is still much work to be done.
"We occupy about 80 percent of the city right now. [There] is still the clearing of each and every house to take away the caches of weapons and to find the stashes of ammunition. So there is much clearing to be done, even though we occupy about 80 percent of the town as we speak," Sattler said.
But while the U.S. military talks of progress in Al-Fallujah, a new front is opening in the northern city of Mosul.
Insurgents there have taken over police stations and residents say gangs of armed men are now patrolling some streets.
Iraqi reinforcements are being sent to the city in a bid to quell the uprising.
Correspondents say the Mosul violence may be a reaction to the Al-Fallujah assault, which has fueled resentment against the U.S. presence.
The military says 22 U.S. and five Iraqi troops have been killed and 170 U.S. soldiers wounded in Al-Fallujah. It puts insurgent losses at 600 dead.
But there are no figures for the civilian death toll in the city -- and aid agencies are increasingly worried about ordinary people trapped there by the fighting.
Today, the spokeswoman for the Iraqi Red Crescent called conditions in Al-Fallujah "catastrophic."
Firdoos al-Abadi said the few families left there are in urgent need of food, water, and medicine. She also expressed concern about the tens of thousands of people in refugee camps outside the city.
A four-truck convoy of aid has left Baghdad for Al-Fallujah.
But the Red Crescent as yet does not have permission to enter the war zone.
For the latest news on Iraq, see RFE/RL's webpage on "The New Iraq".