The continued fighting came as one of the masterminds of the violent insurgency, Jordanian Abu Musab al-Zarqawi, told his supporters to continue the fight and that victory was now certain.
American soldiers claimed advances deep into the southern part of Fallujah, saying most of the remaining insurgents appeared trapped in that part of the city.
"They can't go north because that's where we are. They can't go west because of the Euphrates river and they can't go east because we have a huge presence there. So they are cornered in the south," Marine Master Sgt. Roy Meek told Reuters.
But as forces have pushed deeper into the city, the insurgents are running out of places to retreat, which, according to reporters embedded with advancing American units, has made them more desperate.
"American intelligence officers believe that many of the insurgents have retreated as far as the Shuhada, a relatively modern residential area that is the southernmost neighborhood in Fallujah," Dexter Filkins wrote in Friday's New York Times. "But beyond Shuhada is only the open desert, patrolled by the United States Army. So the insurgents are turning and fighting. And at night, they are setting up deadly ambushes in the moonless pitch blackness of Fallujah's labyrinthine streets."
Despite its advances, skirmishes and battles continued to erupt periodically throughout the city. Midday Friday, Reuters correspondents reported an intense firefight near a mosque in northwest Fallujah, an area American commanders had said was in their control.
Even as American and Iraqi military authorities continued to say the fight for Fallujah was "ahead of schedule," an audiotape, purportedly made by insurgent leader al-Zarqawi, appeared on an Islamist Web site calling on fighters to continue their battle in the city.
"As for you heroes of Islam in Fallujah, praise for your Jihad, praise for your nation, praise for your religion. (Have) one hour's patience, and then you will see the results," the speaker said after identifying himself as al-Zarqawi.
"We have no doubt that the signs of God's victory will appear on the horizon," the speaker continued. "America and those with them felt winds of jihad which will shake their thrones and foundations."
Twenty-two American soldiers and five Iraqis have been killed in the offensive that started Monday. Lt. Gen. John Sattler, commander of the 1st Marine Expeditionary Force, also said 170 U.S. troops had been wounded, although some 40 had already returned to duty after receiving medical treatment.
In other parts of Iraq, insurgent attacks and American and Iraqi responses continued Friday.
Mosul, the third largest city in Iraq, continued to be wracked by sporadic attacks against policy and government buildings. One of the largest Kurdish parties reported an hour-long gunbattle between guards and rebels besieging the complex. Six insurgents were reportedly killed in the fighting.
The attack followed a day of assaults against police stations throughout the city, which killed an unknown number of Iraqi policemen and at least one U.S. soldier. The failure of police to combat the attacks prompted Friday's firing of the city's police chief and authorities in the region had requested additional help from the central government in Baghdad.
"We asked the central government in Baghdad (for reinforcements) and God willing they should arrive today," Gov. Duraid Kashmoula told the Associated Press, adding he believed "there's infiltration among some (security) apparatuses from the saboteurs."
An American military spokeswoman said military efforts would continue to target areas of active resistance in the city.
"Iraqi National Guard and multinational forces are restoring security to those areas of the city where terrorists are attacking from, primarily in the southwestern area," U.S. Captain Angela Bowman told Reuters.
North of Baghdad, American officials said a Black Hawk helicopter had been forced down by enemy fire, the third chopper in two days to be forced to make an emergency landing.
A military spokesman in Baghdad said three members of the four-man crew were injured when the Black Hawk came down hard near the town of Taji, some 12 miles north of Baghdad. Officials said none of the injuries appeared life-threatening.
In Baghdad, insurgents shot dead one U.S. soldier and wounded two others in an ambush on their vehicle in the southern part of the city. Also Al Jazeera broadcast a tape provided by a group calling it self the 1920 Revolution Brigades apparently showing kidnapped American Dean Sadek, a Lebanese American who works at the Baghdad airport. Al Jazeera did not mention any specific threat against Sadek.