President Reagan walked out of Bethesda Naval Medical Center at 6:25 p.m. last Friday evening and flashed a thumbs-up sign, saying he felt "fine." The White House waited an hour, until the television network broadcasts were over, and then issued a statement on Reagan's first major medical examination since last summer's cancer surgery.

The statement reported that three more polyps had been removed from Reagan's intestine and that doctors believed they did not contain cancer. But the statement did not say who the doctors were or how they had reached that conclusion, and did not provide any medical data from the other tests given the president.

Nor would White House officials respond to any questions about his health, even though there appeared to be nothing to hide.

This cautious approach has been in effect since last summer, and it goes to the heart of a debate that may well run through the remainder of Reagan's term, raising troublesome questions about White House credibility and about the conflict between a president's right to privacy and his responsibility to the electorate.

At issue is how much the public should be told about a president's health. Does Reagan, 74, the nation's oldest president, enjoy the same right to a confidential doctor-patient relationship as everyone else? Or should he be expected to give up that right because of the importance of his office?

The questions are laced with political ramifications, too, because Reagan's success over the years has been closely related to his popular image as a buoyant, rugged westerner.

Last summer, when Reagan underwent surgery to remove a cancerous tumor from his colon, the White House provided extensive details about his condition and the operation, including briefings by spokesman Larry Speakes and doctors. The White House was also careful to transfer Reagan's powers to Vice President Bush during the operation.

But since then, the practice has been to give out only limited details about Reagan's health. Several top officials, speaking on condition they not be identified, said this was because First Lady Nancy Reagan has expressed a desire for more privacy. One reason, they said, is that her late adoptive father, Dr. Loyal Davis, was a neurosurgeon who impressed upon her the importance of doctor-patient confidentiality.

Elaine Crispen, press secretary to Mrs. Reagan, said the First Lady was not trying to restrict the flow of information about the president's health and "certainly respects the public's right to know" about it. Rather, she said, Mrs. Reagan was disturbed last summer by comments from other physicians, not involved with Reagan's surgery, about his care. At the time, some of those physicians criticized Reagan's care before the surgery.

Presidential spokesman Larry Speakes said, "Everybody in the White House from President and Mrs. Reagan on down feels very strongly that the public is entitled to know about the health of their president. We have been more forthcoming than any administration in history about the health of the president.

"We do feel, however, all of us, that the bounds of common decency apply even to the president," Speakes added. "We've been careful to give sufficient information so the public knows in great detail the president is capable of performing his duties."

Several doctors agreed that the White House provided sufficient detail about last week's examination, since laboratory tests showed later that the polyps and a small growth removed from Reagan's face were benign.

"All you need is what is being offered now, if they are telling the truth," said Dr. Nelson Trujillo, clinical professor of medicine at George Washington University and a practicing gastroenterologist.

On the question of Reagan's right to privacy, the answers are complex. Although the Constitution provides for a means of presidential succession, it says nothing about polyps. Congress has passed no laws requiring disclosure of a president's medical reports. On minor health matters, at least, Reagan is free to decide for himself what to tell the American people.

"The traditional norm is that the doctor-patient relationship is utterly confidential," said Daniel Callahan, director of The Hastings Center, an organization that studies the ethical problems of medicine and biology. "The critical question is whether when one becomes president you waive the ordinary rights a patient may have, or that the doctors have a lessened obligation."

"It doesn't seem to me that society can declare on its own that the doctor-patient relationship doesn't count," he added. "The patient has to be the one to waive the privilege. It's appropriate that a president do so."

Callahan also said that Reagan chose to give up his right to confidentiality last summer by making extensive disclosures about his illness, and that it might generate unwarranted suspicion to change that now.

"It would seem to me he's within his right," to give out less, he added, "but it doesn't seem practically wise."

Jody Powell, the columnist who was President Carter's press secretary, said, "I don't think a president has much in the way of privacy about things like that. It's a classic conflict of rights -- and there are legitimate arguments on both sides. In the end it always seems to me that a man who has applied for the job of president and been hired -- in his case, you have to resolve those on the side of the public."

Politics and the natural inclination of a White House staff to work to protect a president's image of leadership have always been major factors in such decisions. The picture of Reagan as a wood-chopping, vigorous outdoorsman has been central to his political strength. Aides have taken pains to stress this: Reagan wore a cowboy hat in his official 1980 campaign photo; once elected, he was photographed "pumping iron" for a magazine cover story on physical fitness.

During his 1980 campaign, when Reagan's age became a major issue, he responded with jokes about it and scheduled exhausting campaign trips to demonstrate his vitality. When the issue came up again in the 1984 campaign, he deflected it with a barbed one-liner during his second debate with Walter F. Mondale.

When he was shot in 1981, Reagan again responded with a good humor that may well have contributed to his first-year political triumphs. But it was later disclosed that Reagan's condition was far more serious when he entered George Washington Hospital than his spokesman had revealed.

The turning point appears to have been last summer's surgery, in which two feet of Reagan's lower intestine was removed to stop the spread of a cancerous tumor. Since then, the White House has protected some details about Reagan's medical tests as if they were national security secrets.

Reagan's disclosure three weeks after his surgery that a growth removed from his nose turned out to be a common form of skin cancer followed several days of conflicting and incomplete statements from the White House about it.

Three months later, Reagan responded with exasperation on the subject of cancer when reporters asked him to release the results of his medical examinations. "The whole thing has been portrayed as that I was the sufferer of cancer," he lamented. "I had cancer. And then an operation took place, and now I have a good recovery."