When Israeli Prime Minister Yitzhak Shamir visited the White House last Nov. 29, he was impressed by a previously undisclosed remembrance of President Reagan about the Nazi extermination of Jews during World War II.

Repeating it to his Israeli Cabinet five days later, Shamir said Reagan had told him that he had served as a photographer in a U.S. Army unit assigned to film Nazi death camps.

Shamir said Reagan also informed him that he had saved a copy of the film because he believed that, in time, people would question what had happened. Many years later, as Shamir recalled being told, Reagan was asked by a member of his family whether the Holocaust occurred.

"That moment I thought," Shamir quoted Reagan as saying, "this is the time for which I saved the film, and I showed it to a group of people who couldn't believe their eyes. From then on, I was concerned for the Jewish people."

Shamir's account appeared Dec. 6 in the Israeli newspaper Maariv. It was confirmed last week to Edward Walsh, The Washington Post correspondent in Jerusalem, by Israeli Cabinet secretary Dan Meridor.

On Feb. 15, famed Nazi-hunter Simon Wiesenthal met with Reagan in the White House and heard a similar story. Wiesenthal told Washington Post reporter Joanne Omang that he and Reagan had held "a very nice meeting," during which the president related "some of his personal remarks from the end of the war."

Rabbi Marvin Hier, dean of the Simon Wiesenthal Center in Los Angeles, also was present. He told Omang that Reagan said he was "a member of the Signal Corps taking pictures of the camps" and that he had saved a copy of the film and shown it a year later to a person who thought the reports were exaggerated.

"He said he was shocked that there would be a need to do that only one year after the war," Hier said.

There is no reason to doubt Reagan's concern about the plight of the Jews in World War II. He has spoken out consistently about the horrors of the Holocaust and has supported Israel since the founding of the Jewish state.

But it is equally indisputable that Reagan never filmed a Nazi death camp. Reagan, who had a commission in the cavalry reserve, was called to active duty in April, 1942. After brief service at Fort Mason in San Francisco, he spent the war with the First Motion Picture Unit of the Army Air Corps, making training films in Hollywood and living at home.

Over the years, other dramatic accounts related by Reagan have been questioned. The best known is a story of a pilot who rode down in his B17 bomber with a wounded gunner rather than bail out and save himself.

But a more curious story, which Reagan used to tell about himself, is of a high school football game between his Dixon, Ill., team and rival Mendota. Reagan's account is that Mendota accused Dixon of committing an infraction and that the referee asked Reagan if he had committed it.

"I told the truth, the penalty was ruled and Dixon lost the game," Reagan used to say. There are no other known accounts of this incident. The only game that Dixon lost to Mendota when Reagan played was by a 24-0 score.

The White House, ever sensitive to suggestions that Reagan embellishes, did not react lightly to queries about the Shamir and Wiesenthal accounts. Robert Sims, a normally mild-mannered deputy press secretary, said, "There's no story here--the only story is that The Post is out to make Reagan look bad."

Subsequently, White House chief of staff James A. Baker III asked Reagan about the meetings with Shamir and Wiesenthal. Reagan told him that he "never left the country" during World War II and "never told anyone that he did."

The president's account was that he had seen a film of the death camps while working on a training movie, remembered that World War I atrocities had been questioned and "didn't want atrocities against the Jewish people to be forgotten." So he kept a copy of the film and, when "a Jewish friend" questioned him about it a year or two later, showed him the copy.

Sims said that the recollections of Secretary of State George P. Shultz, who was present at the Shamir meeting, and Marshall Breger, an administration official who attended the Wiesenthal meeting, support the president.

How could Shamir and Wiesenthal, fluent in English and known for their grasp of detail, have misunderstood so completely what Reagan said to them in two different meetings more than two months apart? What Jew would doubt the existence of the Holocaust?

The story in any of its versions was new to this reporter, who, in the course of preparing two biographies and interviewing many persons who knew Reagan during his World War II days, had never heard it. There is no reference to it in any other Reagan biography nor in his autobiography. It is a story that no one seems to have heard.

Reaganism of the Week: Speaking to the National Alliance of Senior Citizens last Wednesday, Reagan said: "You know, I've been around awhile myself . . . . Just to show you how youthful I am, I intend to campaign in all 13 states."