For the first time, researchers have strong evidence that the drug AZT can significantly delay the onset of AIDS in people showing mild symptoms of immune system damage.

AZT, or azidothymidine, is now the only medication licensed for the treatment of AIDS, but it has been approved for use only in the sickest patients. Until now, AZT had been shown to be effective only in patients who already had full-fledged AIDS or certain other symptoms, including severely debilitated immune systems. The new research indicates that AZT can delay the onset of AIDS in patients who are just starting to show symptoms of decline in the immune system.

As many as 100,000 to 200,000 Americans infected with the AIDS virus have mild symptoms like those of the patients in the study, said Dr. Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, which sponsored the study. Supplies Termed Adequate

Dr. Fauci added that the new data should encourage many more people to be tested to see if they are infected with the AIDS virus before they show symptoms of disease.

Kathy Bartlett, a spokeswoman for Burroughs Wellcome, the manufacturer of AZT, said the company had adequate supplies of the drug to treat the patients with mild symptoms. A year's supply of AZT costs about $7,000, Ms. Bartlett said.

Government health officials estimate that 40,000 Americans have full-fledged AIDS and would qualify for AZT under the current standards, and that about 25,000 were taking it. First Clinical Evidence

Although AZT does not cure AIDS, it does slow the multiplication of the virus. Many doctors had suspected that the drug would benefit patients who were not severely ill, but until now they had no clinical evidence.

''This is the first clear proof that early intervention makes a difference,'' said Dr. Jerome Groopman of New England Deaconess Hospital in Boston. ''It's exciting and it's a finding of real importance.''

Another Federal study is under way concerning the effects of AZT on people infected with the AIDS virus but with no symptoms of disease. It has not yet demonstrated a difference between participants who took AZT and those who did not, Dr. Fauci said. Federal health officials estimate that a million to 1.5 million Americans are infected with the AIDS virus but have no symptoms of disease. #713 People in Study The study of people with mild symptoms began in August 1987 and was coordinated by Dr. Margaret Fischl of the University of Miami and conducted by investigators at 29 medical centers. It involved 713 people who were infected with the AIDS virus and had one or two symptoms, like intermittent diarrhea; thrush, which is a fungal infection of the mouth, or a chronic rash.

The patients in the study also had mildly debilitated immune systems, as shown by their counts of T-4 cells, disease-fighting white blood cells of the immune system that the AIDS virus kills. A normal T-4 cell count is 800 to 1,200 cells per cubic milliliter of blood. Patients with full-fledged AIDS have T-4 cell counts that are lower than 200. The patients in the study had T-4 cell counts of 200 to 800.

Half the patients in the study took AZT and the rest took a dummy pill. So far, 36 patients taking the inert substance have progressed to full-fledged AIDS but only 14 of those taking AZT developed the full disease. Few Serious Side Effects

In addition, Dr. Fauci said, ''Only a very small percentage of the patients taking AZT had serious side effects -less than 5 percent.'' When patients with full-fledged AIDS take AZT, as many as 50 percent have to discontinue the drug because of severe side effects, including pronounced anemia.

''This clearly shows that early intervention is important,'' Dr. Fauci said. ''People should be tested to see if they are positive and should pay attention to symptoms.''

Dr. Sandra Nusinoff Lehrman, head of the department of antimicrobial therapy at Burroughs Wellcome, said she learned about the results Wednesday evening, when the study's data monitoring committee decided to end the study because AZT was showing an effect.

She said Burroughs Wellcome would be meeting with the Food and Drug Administration to try to expedite the marketing approval of AZT for patients like those in the study. ''We will work very closely with the F.D.A. to get all the data analyzed and reviewed as soon as possible,'' Dr. Lehrman said. Findings Called 'Very Exciting'

Doctors and advocates for AIDS patients were elated by the study results. ''This sounds very exciting,'' said Dr. Nathaniel Pier, a New York doctor with a large AIDS practice. ''It's going to help us clinicians a lot. It confirms the clinical consensus that early intervention is logical and helps answer the question of what to use to intervene.''

Dr. Pier said many people had been reluctant to be tested to see if they were infected with the AIDS virus because they hesitated to face the possibility that the test would show infection and that they would simply have to wait for the inevitable serious illness. If people can have a treatment that is demonstrated to slow the progression of an AIDS infection, they may be more willing to have AIDS tests, Dr. Pier said.

Richard Dunne, executive director of the Gay Men's Health Crisis in New York, said the new finding put AIDS treatment into ''a new age.''

''We have always argued that early intervention made sense, but now we have data, very strong compelling data, that shows it,'' he said.

Mr. Dunne said the next challenge would be to ''develop plans and resources in a very short period of time to deliver this information and follow it up with services,'' including AIDS testing and counseling and insurance coverage for people who might benefit from AZT.