The study found that those who average more than 90 grams of fat a day have roughly double the risk of those who eat just 37 grams.
However, the finding is likely to be controversial, since it contradicts many large, careful studies that found no link between what women eat and their risk of this common cancer.
Researchers who conducted the latest study argue theirs is better, because it used a more precise method of measuring women's typical diets. However, others said the study is too small to overturn the vast research suggesting diet plays little or no role in breast cancer risk.
The study, published in this week's Lancet medical journal, was conducted at Cambridge University in England and involved 13,070 women who kept diet records from 1993-97.
The researchers set out to discover whether the reason the previous follow-up studies found no link was that the method they used to examine dietary habits - a food frequency questionnaire - was too inaccurate. They also had the women keep a daily diary in which they recorded everything they ate.
By 2002, 168 of the women had developed breast cancer. Each of those cases was matched with four healthy women of the same age who had filled out the questionnaires and diaries around the same time as the women who developed breast cancer had.
The total group was divided into five equal categories of about 170, according to how much fat they ate each day. Two methods were used to place the women in one of the five categories; one based on the questionnaire and one on the daily diary.
The researchers calculated separately for both methods the difference in breast cancer risk between the women who ate the least fat and those who ate the most fat.
"The effects just weren't seen with food frequency questionnaires," said investigator Sheila Bingham, deputy director of the human nutrition unit at Cambridge University. She called the questionnaire a "very crude method" that was not reliable.
However, when the food diaries were used to categorize the women, those who ate the diet highest in saturated fat were twice as likely to develop breast cancer as those who ate the least.
Of those in the lowest category, 14 percent developed breast cancer, compared with 20 percent, in the highest class. The more fat that was consumed, the higher the risk of breast cancer.
Women who ate a higher-fat diet were not necessarily fatter; but once the researchers adjusted the results to eliminate skewing by other factors promoting breast cancer, such body weight and total calories eaten, the women who ate the most saturated fat had twice the breast cancer risk as those who ate the least.
Most of the fat in the women's diets was saturated fat, so the findings for total fat intake were similar.
Marji McCullough, an epidemiologist at the American Cancer Society, said researchers disagree over whether a questionnaire or food diary is more accurate.
Furthermore, the number of cancer cases in the latest study is small as such research goes. A recent analysis combined over 7,000 cancer cases in eight studies and found no risk from fat.
"If you consider all the evidence right now, you would assume there is a very small or no effect of fat on breast cancer," she said.
However, Dr. Elio Riboli, a nutrition and cancer expert, said, "These results reopen entirely the issue of the importance of investigating more, and with better data, the saturated fat-breast cancer hypothesis."
The chance of a woman developing breast cancer sometime during her life is between 8 percent and 11 percent, according to the World Health Organization.
"This article is a major step in the torturous process of identifying the dietary determinants of breast cancer," said Riboli, who works with the U.N.'s International Agency for Research on Cancer. "Doubling or reducing by 50 percent the risk would make a huge impact on the suffering of tens of thousands of women each year."
Many early studies that looked back at the diets of breast cancer patients and compared them with the eating habits of healthy women of the same age found that a diet high in fat, or saturated fat - fat that comes from animal-based food such as meat, fish and dairy products - was weakly associated with a modest increase in breast cancer risk.
Experiments in lab animals also indicated that high fat intake could increase the likelihood of breast cancer.
However, most of the recent studies, which followed groups of healthy women over time, failed to find a link.
By Emma Ross