Al-Fallujah doctors tell news agencies that some 600 Iraqis, including civilians, have been killed and nearly 2,000 wounded in the siege of the town.
Some Iraqi politicians are accusing U.S. troops of using disproportionate force and heavy-handed tactics in the city. The U.S. military say figures for civilian deaths are impossible to verify and that its soldiers are obeying international law and are not targeting civilians.
Bassam Abdel Kader is an assistant to Rafa al-Isaavi, a doctor working in Al-Fallujah. Kader says he has been making trips from Al-Fallujah to Baghdad to bring back medicine to the city. He says he cannot give any firm numbers for those killed or injured in Al-Fallujah, but does accuse U.S. troops of indiscriminately bombing the town.
"The numbers [of casualties] are big because of indiscriminate American bombing, which hits civilian houses. There are many children and old people killed because of this indiscriminate shelling," Kader says.
The U.S. military strongly denies the charges. U.S. General John Abizaid is head of U.S. forces in Iraq.
"We've been attacking to secure the city of Fallujah, and we're running into active resistance. It is very clear where we're taking fire from -- and where we're taking fire from, we're applying the appropriate, proportionate combat power to eliminate that resistance. We are being very deliberate and precise in the application of that combat power to prevent any wounding or injuring of noncombatants in the area," Abizaid says.
U.S. military spokesman Brigadier General Mark Kimmitt says insurgents in the city are using Iraqi civilians as human shields and are firing weapons at U.S. forces from inside schools, mosques, and hospitals.
There is no independent confirmation of these claims, nor of the number of Iraqi civilian deaths in Al-Fallujah.
The U.S. operation in Al-Fallujah is cause for growing concern among members of the U.S.-appointed Iraqi Governing Council. Last week, the council issued a statement calling for an immediate cease-fire and for political negotiations in some parts of the country, particularly in Al-Fallujah.
Last week, a Sunni member of the Governing Council, Ghazi Ajil al-Yawir, threatened to resign unless the coalition peacefully resolves the crisis in Al-Fallujah. There are reports of other council members also threatening to suspend participation or tendering their resignations.
Mahmud Uthman, an independent Kurdish member of the Iraqi Governing Council, tells RFE/RL that he believes the U.S. is using disproportionate force in Al-Fallujah. He calls it a "collective punishment, a total punishment of the whole town."
"I want them to use force to end terrorism, [to fight] terrorists. But, of course, using that excessive force against a town of 300,000 people and then having all those killings and wounded and everything, [having] destruction because terrorists are [inside] is unacceptable. This is not acceptable. It's against any law," Uthman says.
The U.S. military says the aim of the operation in Al-Fallujah is to arrest those who killed and mutilated four American civilian contractors at the end of March. But Uthman says the U.S. military is using force indiscriminately and that the entire population of Al-Fallujah is suffering.
"When you use force and all weapons against a town, you can't discriminate. You don't know who those people are [you are using the force against]. The question is, the people, terrorists or even [Muqtada] al-Sadr people, the people who are [fighting the United States], they are in between the population. They are in the towns. They are among the population. They are not in the desert. They are not in the mountains. They are not in a separate place," Uthman says.
He says U.S. troops should have first surrounded Al-Fallujah, allowed the civilian population to leave, and only then started attacking or looking for those guilty of the killings.
Unfortunately, Uthman says, civilians in Al-Fallujah were allowed to leave only after several days of fighting had already occurred. He says civilians have had to endure aircraft, artillery, and tank fire. As a rule, he says, casualties among the civilian population have been much higher than among the anti-American fighters. He says the anger that is growing against the United States because of such tactics is what the militants seek most.
On 11 April, the British newspaper "The Daily Telegraph" quoted a senior British officer in Iraq as condemning U.S. military tactics in Al-Fallujah. The officer -- who did not give his name -- said the U.S. military's use of force "is not proportionate and is over-responsive to the threat they are facing."
The officer also said that, under British military rules of war, British troops would never be given clearance to carry out attacks similar to those being conducted by the U.S. military in Al-Fallujah, in which helicopter gunships have been used on targets in urban areas.
The U.S. strongly insists its attacks in Al-Fallujah have been well-targeted and are not designed to punish the city's residents.
U.S. Brigadier General Mark Kimmitt says: "It is not the practice of the coalition forces -- any of the coalition nations -- to exercise collective punishment or collective action on a city. That is just not done. It is not practiced, and it violates international law."
Uthman says U.S. tactics are leading to defeat in the fight for the hearts and minds of the Iraqi people.
"They have lost it [the battle for opinion] quite heavily,” Uthman says. “There are still some Iraqis supporting them, but very, very few, except in the Kurdish area where people are not against them. That's because they haven't ruled the Kurdish area directly. There has been no punishment there. There is no problem."
The U.S.-led coalition says it understands the problems some members of the Iraqi Governing Council are facing. U.S. officials say they recognize that members of the Governing Council are under increasing pressure from the communities they represent.
(Sami Alkhoja in Baghdad contributed to this story.)