Eight soldiers were also wounded in Monday's fighting while a mosque was damaged after US tanks and aircraft targeted fighters believed to be inside, said the occupation force's deputy operations director, Brigadier General Mark Kimmitt.
A CNN journalist embedded with US troops in Falluja reported that at least 10 marines had been injured. Many of the American casualties reportedly came after more than 100 Iraqi fighters attacked a US patrol.
Aljazeera's correspondent in the besieged Iraqi city, Abd Al-Adhim Muhammad, witnessed a US helicopter attack on Falluja's Golan district. Muhammad said two residents were taken to hospital moments after the first attack.
US occupation soldiers pounded two districts with heavy machine gun fire, local residents said. Skirmishes in the Golan and Shuhada districts broke out around 11:20 am (07:20 GMT) and have continued through the day.
Falluja has proved a hotbed of resistance to the occupation, with the US claiming a small group of foreign fighters is stoking clashes with troops.
Appeal to UN
Despairing at a largely ignored peace pact, town elders have written to UN Secretary-General Kofi Annan asking him to mediate between resistance fighters and occupation forces.
They also urged Annan to set up an international investigation into the US-led occupation of Iraq.
Kofi Annan has been urged to
investigate US actions
Speaking on behalf of the Falluja town council, Muhammad Tariq Abd Allah said some of the council had "met UN officials at the Amman office of the UN special envoy, Ross Mountain, and given them a message for the UN secretary-general asking for his mediation.
"We told the UN people that if this mediation works, we are ready to ensure that the people of Falluja will turn in their heavy weapons and respect any agreement reached," he said.
Abd Allah stressed it was important the UN appoints a neutral mediator "who will give us guarantees that the Americans will also respect their end of the agreement".
The Falluja delegation chief, Shaikh Muhammad Hamad al-Shihan, said he wanted the UN to know of the terrible hardship in Falluja since the occupation began.
"The human rights violations that happened in Falluja are very serious and the massacres that happened there are unprecedented"
Falluja delegation leader
"We are facing what can be called ... war crimes, and the situation can no longer bear the actions of the occupation forces who are behaving outside all international laws."
Al-Shihan also urged Annan to intervene quickly "personally to stop the bloodbath".
"The human rights violations that happened in Falluja are very serious and the massacres that happened there are unprecedented," he said.
The US marines launched their offensive on 5 April after the murder of four US civilian contractors 50km west of Baghdad.
Iraq's interim health minister, Khudayr Abbas, said that by Thursday, 271 Iraqis had been killed in the city.