In one case, a pregnant woman and her child died in a refugee camp west of the city after the mother unexpectedly aborted and no doctors were on hand, Firdus al-Ubadi, an official from the Iraqi Red Crescent Society, told Reuters on Wednesday.
In another case, a young boy died from a snake bite that would normally have been easily treatable, she said.
"From a humanitarian point of view it's a disaster, there's no other way to describe it. And if we don't do something about it soon, it's going to spread to other cities," she said.
About 10,000 US soldiers and 2000 Iraqi troops are fighting to wrest control of Falluja, 50km west of Baghdad.
Families fleeing Falluja
At least 2200 families have fled Falluja in recent days and are struggling to survive without enough water, food or medicine in nearby towns and villages, she said.
"This is not a joke, it is a full-scale battle. The battleground is horrific even for us soldiers, so imagine how civilians feel"
Major General Abd al-Qadir Mohan, Iraqi military spokesperson
Some families have fled as far as Tikrit, about 150km north of Falluja.
But the biggest concern is people in and around Falluja itself - they can't be reached because US and Iraqi forces have set up a wide cordon around the city to prevent anyone from entering and exiting the city
It is unclear how many civilians are left in Falluja, but the Association of Muslim Scholars estimates about 60000 people are still there while the US military says 150,000 (half the entire population) had fled since October.
Due to the chaos, however, no official numbers are available.
Trapped at home
Between a nightly curfew and the danger of venturing onto the streets, many Iraqis are effectively trapped at home.
"We've asked for permission from the Americans to go into the city and help the people there but we haven't heard anything back from them," Ubadi said. "There's no medicine, no water, no electricity. They need our help."
|Red Crescent officials say women |
and children need most assistance
"Our first mission is to obtain permission from the multinational forces to enter the city and start evacuating the wounded, the elderly, the children and women," she explained.
The Red Crescent Society has teams of doctors and relief experts ready to go in to each of Falluja's districts with essential aid, but needs US approval first.
The US military was not immediately available to comment on the aid agency's request, but has said its first priority is to defeat the fighters in Falluja.
Iraq's military spokesman for the assault, called Operation Dawn, admitted that conditions inside the city for the few residents still living there were grim.
"This is not a joke, it is a full-scale battle," Major General Abd al-Qadir Mohan told reporters at Camp Falluja, outside the city.
"The battleground is horrific even for US soldiers, so imagine how civilians feel," he said.
An attack was launched late on Monday which has since turned into furious street-to-street fighting.
Young boy killed
On Tuesday, a 9-year-old boy died after being hit in the stomach by shrapnel. His parents were unable to get him to hospital because of the fighting and so resorted to wrapping a sheet around him to stem the blood flow.
"From a humanitarian point of view it's a disaster, there's no other way to describe it. And if we don't do something about it soon, it's going to spread to other cities"
Iraqi Red Crescent Society
He died hours later of blood loss and was buried in the garden of the family home.
"We buried him in the garden because it was too dangerous to go out," said his father, teacher Muhammad Abbud. "We did not know how long the fighting would last."
The International Committee for the Red Cross says there are thousands of elderly and women and children who have had no food or water for days. At least 20,000 have gathered in the town of Saqlawiya, south of Falluja.
"The Red Cross is very worried. We urge all combatants to guarantee passage to those who need medical care, regardless of whether they are friends or enemies," spokesman Ahmad al-Raoui said. "They must be allowed to return home as soon as possible."
Aid workers say there are still hundreds of families left in the city, which has been pummelled by sustained aerial bombardment and artillery fire in recent days.
"We know of at least 157 families inside Falluja who need our help," said Ubadi.
For some it is already too late.
One mother and her three daughters had intended to flee but their home was hit by a bombardment earlier this week and all died, neighbours who escaped told aid workers.