The Food and Drug Administration yesterday proposed taht all liquied protein products, used primarily by dieters, carry a warning that they "may cause serious illness or death."

The FDA proposal comes at a time when that agency and the federal Center for Disease Control are studying reports of the deaths of 31 persons, in various areas of this country and Canada, who were on the popular diet.

The FDA must wait 30 days for public comment on the proposed ban before ordering the change in labeling of the product, which is used by thousands in the Washington area and by an estimated 2 to 4 million persons in this country and Canada.

The proposal FDA labeling for the popular products reads:

"WARNING - Very low calorie protein diets may cause serious illness or death.DO NOT USE FOR WEIGTH REDUCTION OR MAINTENANCE WITHOUT MEDICAL SUPERVISION. Do not use for any purpose without medical advice if you are taking medication. Not for use by infants, or pregnant or nursing women."

"If we determine that the risk to consumers cannot be controlled by labeling, then FDA will act to remove the products from the market," FDA Commissioner Donald Kennedy said in a prepared statement.

Of the 31 deaths now being studied by the FDA and CDC, 10 have been officially ruled to have a possible connection with the use of thdiet products.

The CDC has stressed, however, that it is not yet possible to determine whether the deaths, all due to heart problems, were caused by the diets or underlying medical conditions.

On Wednesday, Los Angeles area physicians informed the annual meeting of the American Heart Association of the deaths of two women, and illness of a third, all of whom developed severely irregular heart rythyms while on the liquid protein diet.

"It should not be used as the sole source of calories for anybody," said Dr. J. Michael Criley, of UCLA. "I think most physicians are over their heads in trying to manage this. Even in the best of hands, these patients cannot be managed when they start a downhill slide . . . There is nothing magical about the liquid protein diet except that it's a form of starvation that's become a fad."

The three women, who ranged in age from 27 to 35, were described as previously healthy individuals - except for their obesity - who each lost between 80 and 90 pounds.

The liquid protein is a so-called "modified fast" diet, which means that the person is fasting, going without food, except for the 300 to 500 calories they drink a day in the form of liquid protein.

It is the theory of the diet's supporters that the person on the diet will burn up fatty tissue, but not protein or muscle tissue, because of the supplementary liquid protein.

Additionally, persons under close medical supervision receive vitamins and minerals designed to replace those substances, which they would normally get through eating normally.

Most experts agree that if the liquid protein diet is responsible for any deaths, the liquid protein itself is not the culprit. Rather, the patients may not have been getting the minerals, such as potassium, necessary to keep the hearts electrical system in proper balance.

If the electrolytes - substances that include potassium, calcium and magnesium - are not kept in proper balance, the electrical charge that triggers the action of the heart does not function properly, and the heart gets out of phase, failing to properly circulate the blood.

Dr. William Ayers, the medical director of the Georgetown Weight Management program at the Georgetown University Medical Center - a program that does not use liquid protein - said he was quite sure the deaths were not caused by the great weight losses.

"We've had a handful of patients in the same weight range with whom we've had zero problems," said Ayers. "I have no idea what's happening to the patients" on the diet, he said, but then added that the problem was likely to be caused by an "electrolyte imbalance."

Dr. Robert Linn, a Philadelphia physician who popularized the diet with his book "The Last Chance," yesterday defended the liquid protein regimen, saying he'd always understood that a person or thing was "innocent until proven guilty . . . How lucky can I be treating 3,000 patients and not having a fatality."

Linn, who has five Robert Lim Medical Associates clinics in Washington, Pennsylvani, Delaware and New York, said "how a CDC scientific study could be so sensationalized is beyond my belief . . . How many obese patients are going to die because they are scared away by scare headlines? he asked rhetorically. "How many lives are going to be saved because of this diet?"

Linn said, however, that he is all for the development of regulations regarding the sale of the diet supplements, which he said he is not associated with in any way:

In fact, when asked if the products should be sold only on the prescription of a physician, Linn, who states repeatedly in his book that the diet should only be undertaken under the supervision of a doctor, said "if it's the only way that it can be handled, let it be handled this way."

Patients at Linn's Washington clinic, which treats about 100 persons a week, are charged $60 a week for the diet, physician subervision, and behavior modification designed to change their eating habits when the diet is over.