Administration health officials and the American Cancer Society yesterday disputed vehemently a federal cancer official's contention that smoking limited numbers of certain "less hazardous" cigarettes is "tolerable" from a health standpoint.

But the official, Dr. Gio Batta Gori, Deputy director for cancer cause and prevention at the National Cancer Institute stood firmly by his conclusion. He said in an interview that his superiors are under pressure from Health, Education and Welfare Secretary Joseph A. Califano Jr. to fire him.

Cancer Institute officials denied that there has been any pressure to get rid to Gori, but they joined with Califano and other leaders in the health field in decrying Gori's conclusions.

They said there is no proof yet for his belief that not every smoker but the "average" one who smokes no more than three to 23 cigarettes daily of some brands now on the market should suffer no more extra risk of death from any cause than those who smoked only two cigarettes a day before 1960, when all cigarettes were far more dangerous.

Gori said so much tar, nicotine and other chemicals have been eliminated from cigarettes or cigarette smoke that from three to 23 cigarettes of certain brands contain no greater amounts of these chemicals than just two pre-1960 cigarettes. Gori called these smoking levels not safe but "tolerable," meaning the incidence of disease and death would be greatly reduced, though not eliminated.

The health officials said his use of the word "tolerable" in a general population or public health sense would mislead Americans into thinking cigarettes are safe for them as individuals.

"There is no such thing as a safe cigarette" or anything like it and leading government scientists are "all very disturbed" over the fear that millions of people might think so, said Califano, who last January started his own drive to halt cigarette smoking.

Surgeon General and Assistant HEW Secretary Julius Richmond and the heads of HEW's two biggest research units - the Cancer Institute and the National Heart, Lung and Blood Institute - all attacked Gori's "assumptions" that anyone can smoke any number of cigarettes whatsoever at low risk.

Dr. Arthur Upton, Cancer Institute head, said Gori's use of the word "tolerable" was "unfortunate." Gori's statements have "set back our cause, and even if we can correct the misinterpretation, we will have lost valuable Momentum," he said.

In further response to the unusual attacks on his conclusions - scheduled to be published in the Journal of the American Medical Association - an upset Gori said in an interview:

"Califano is very hot on his own campaign, so he is putting pressure on the National Cancer Institute to have me disciplined or dismissed or something."

Upton, asked by The Washington Post if the intended to keep Gori in his present job, said, "I have been talking to Dr. Gori" about a change "ofr perhaps three months," because Gori, a deputy director since 1975, and his new superior, Dr. Gregory O'Conor, "simply haven't found a comfortable working relationship."

But Upton said "there is absolutely no substance" to any contention of pressure from Califano. He said, "I've spoken to the secretary several times today" about this matter, and "at no point has he indicated or asked that Gori was to be disciplined or demoted."

Upton said he had told Gori "that the secretary is upset" and "that the report tends to counteract the secretary's initiative on smoking." But any change in Gori's job, Upton said, will have "nothing to do with his report," since "I knew nothing at all about it until yesterday."

Dr. Sidney Wolfe, head of the Ralph Nader Health Research Group, said Gori should be fired for "the most damaging statement that has been made about smoking in the last 10 years." He called Gori's words "reckless," and said "we have no idea yet what chemicals in cigarette smoke are the dangerous ones," or "what the manufacturers' increases of all sorts of chemicals additives for flavor" will do, or whether lower doses of some chemicals will just take longer to cause disease.

Still, Dr. Arthur Holleb, American Cancer Society medical director - while saying "there is no such thing as a proven safe cigarette" - agreed that low tar and nicotine cigarettes impose less serious risks of lung cancer and other diseases.

Dr. Lawarence Garfinkel, Cancer Society vice president and statistician, said that in two five-year periods - 1960-65 and 1966-72 - there was a 16 percent drop in mortality from all diseases, a 14 percent drop in heart disease mortality and a 26-percent drop in lung cancer mortality in a million male smokers followed by the society.

It was statistics like these that made Gori conclude that further improvements in cigarettes would reduce deaths not only from cancer - his own field - but from heart disease, pulmonary emphysema and other smoking-linked ills.

He said these drops were "far from conclusive," but did indicate "some effect" of less dangerous cigarettes. Dr. Ernest Wynder, president of the American Health Foundation and well-known cancer scientist, agreed that "it is reasonabel to expect some reduction in risks" as cigarettes are made less dangerous.

Gori said the health leaders were themselves misinterpreting his statements. These made it clear that only one brand, Carlton Menthols, is now so low in toxins that by he calculation most persons would smoke 23 cigarettes daily with no measurable risk beyond a non-smoker's. He said the average smoker might similarly consume 18 Now Menthols, 17 Nows or Strides or 16 Carletons without added problems so far as large-scale statistical studies could detect.

But his co-worker, Dr. Cornellius Lynch, said these brands currently represent less than 2 percent of all cigarettes sold - and other "less hazardous" but not nearly as clean cigarettes represent only another 18 percent.

This led Holleb to call on the tobacco industry to stop making more hazardous brands and exercise its "demonstrated ability" to make better products.