Our correspondent also saw children in the city who were suffering from paralysis or brain damage - and a photograph of one baby who was born with three heads.
He adds that he heard many times that officials in Fallujah had warned women that they should not have children.
Doctors and parents believe the problem is the highly sophisticated weapons the US troops used in Fallujah six years ago.
British-based Iraqi researcher Malik Hamdan told the BBC's World Today programme that doctors in Fallujah were witnessing a "massive unprecedented number" of heart defects, and an increase in the number of nervous system defects.
She said that one doctor in the city had compared data about birth defects from before 2003 - when she saw about one case every two months - with the situation now, when, she saw cases every day.
Ms Hamdan said that based on data from January this year, the rate of congenital heart defects was 95 per 1,000 births - 13 times the rate found in Europe.
"I've seen footage of babies born with an eye in the middle of the forehead, the nose on the forehead," she added.
A spokesman for the US military, Michael Kilpatrick, said it always took public health concerns "very seriously".
"No studies to date have indicated environmental issues resulting in specific health issues," he said.
"Unexploded ordinance, including improvised explosive device... >>>
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