They said, in interviews with The Independent, that as well as deaths from bombs and artillery shells, a large number of people including children were killed by American snipers. US forces refused repeated calls for medical aid for injured civilians, they said.
Some of the killings took place in the build-up to the assault on the rebel stronghold, and at least in one case - that of the death of a family of seven, including a three-month baby - the American authorities have admitted responsibility and offered compensation.
The refugees from Fallujah describe a situation of extreme violence in which remaining civilians in the city, who have been told by the Americans to leave, appeared to have been seen as complicit in the insurgency. Men of military age were particularly vulnerable. But there are accounts of children as young as four, and women and old men being killed.
The American authorities have accused militant sympathisers of spreading disinformation, and have also claimed that people in Fallujah have exaggerated the number of casualties and the level of damage in the air campaign that preceded the assault.
The US military, which is inquiring into last week's shooting of an injured Iraqi fighter in Fallujah by a US marine, has said that any claims of abuse will be investigated. They also maintain that the dead and injured civilians may have been victims of insurgents.
The claims of abuse and killings, from different sources, appear, however, to follow a consistent pattern. Dr Ali Abbas, who arrived in Baghdad from Fallujah four days ago, worked at a clinic in the city which was bombed by the Americans. He said that at least five patients were killed.
The doctor said that the attack took place despite assurances from American officers that they were aware of its location and would ensure that it was spared military action.
Dr Abbas, 28, said: "We had five people under treatment and they were killed. We do not know why the clinic was hit. Our colleagues from the Fallujah General Hospital, which was further out in the city, had talked to the Americans and had told us that they would avoid attacking us.
"Afterwards myself and other members of staff went from house to house when we could to help people who had been hurt. Many of them died in front of us because we did not have the medicine or the facilities to carry out operations. We contacted the doctors at the Fallujah hospital and said how bad the situation was. We wanted them to evacuate the more badly injured and send drugs and more doctors. They tried to do that, but they said the Americans stopped them.
"One of things we noticed the most were the numbers of people killed by American snipers. They were not just men but women and some children as well. The youngest one I saw was a four-year-old boy. Almost all these people had been shot in the head, chest or neck."
The family of Aziz Radhi Tellaib were killed before the battle for Fallujah began. He had been driving them to Ramadi to visit relations when the car was hit by fire from an American Humvee and careered into a tributary of the Euphrates.
Mr Tellaib freed himself but could not save the rest of the family. Those who died included Mr Tellaib's wife Ahlam, 26; his sons Omar, seven, and Barat, three, and his daughter Zainab. Also killed were his niece Rokyab, 26, her three-year-old son Fadhi, and three-month-old daughter Farah.
Mr Tellaib, 33, a merchant, said: "We were stopped, in a line of cars, by some Humvees which had overtaken us. One soldier waved us forward, but as I drove up there was firing from another Humvee. I was shot in the side of the head, and my wife and elder son were shot in the chest. I think they must have died then. There was blood all over my eyes. I lost control of the car which fell into the river. I managed to get out, and then tried to get the others out, but I could not and the car sank.
"The Americans told the police that it was all a mistake, and I could get compensation. But what about my family? My life has gone. They might as well have killed me as well."
Rahim Abdullah, 46, a teacher, said that anyone in the street was regarded by the Americans as the enemy. "I was trying to get to my uncle's house, waving a piece of white cloth as we had been advised when they started shooting at me. I saw two men being shot. They were just ordinary people. The only way to stay alive was to stay inside and hope your house did not get hit by a shell."