The military said U.S. and Iraqi forces have "fought their way through half of the city," including the Jolan district, which is suspected to be the center of insurgent activity.
The U.S. military said at least 71 insurgents have been killed so far.
As the fighting goes on, Iraqi government spokesman Tha'ir al-Naqib said that "many armed groups" in Al-Fallujah have asked to surrender and that the government will extend amnesty to those groups who have not committed "major crimes."
Iraqi General Abd al-Qadir Mohan, commander of Iraqi forces, today said his troops have found buildings in Al-Fallujah where numerous foreign hostages were held and killed. Mohan described the buildings as "hostage slaughterhouses."
Meanwhile, the group that has seized three relatives of interim Iraqi Prime Minister Iyad Allawi, Ansar Al-Jihad, has threatened to kill them unless Allawi halts the Al-Fallujah offensive.
Also today, a curfew was declared in the northern city of Mosul due to an escalation in violence.
(Reuters/AFP/AP)[For the latest news on Iraq, see RFE/RL's webpage on "The New Iraq".]