Reagan administration executives meeting privately at the Pentagon last month warned that prosecuting young men who refuse to register for the draft might fire up anti-nuclear groups and suggested that any such trials be held in remote areas of the country, not Washington, D.C., according to a transcript of the meeting obtained by The Washington Post.

The transcript also shows Edwin Meese III, President Reagan's counselor, taking considerable interest in prodding registrations by denying such federal benefits as college loans and unemployment payments to men who refused to register.

The rare inside look provided by the transcript, which was not meant for public release, portrays an administration trying to find a way to wipe out the embarrassing backlog of 527,000 non-registrants without at the same time kicking up new political storms for itself by holding highly visible trials.

"My feeling is that felony prosecutions at this time may have an awful lot to do with the anti-nuclear movement," said John S. Herrington, assistant secretary of the Navy for manpower. "I think we ought to proceed really cautiously on this particular point. This would be a real rallying point. I am not in principle against felony prosecutions for this . . . . I think the cases should be quiet; and pick the right jurisdiction so you don't end up in New York or Chicago, and end up in Omaha or somewhere like that for your first few trials."

"Not the District of Columbia," said Defense Secretary Caspar W. Weinberger, who chaired the April 12 meeting.

"There can't be any selective prosecution, but I understand there is prosecutorial discretion, and I have got some names," said Selective Service director Thomas K. Turnage, a retired major general.

"Actually," said Weinberger, "that is somewhat out of our hands because we could make recommendations, if we wished to do so, about urging Justice to exercise this discretion in view of current situations and all, but we can't interpose ourselves on them since a felony has been committed, or at least we have reason to believe it has."

Although opposing compulsory draft registration as a presidential candidate, Reagan reversed himself in January and said he would keep the requirement he inherited from the Carter administration. He gave those who had failed to sign up until Feb. 28 to do so.

Men born in 1960 and subsequent years are required to go to their local post offices within 30 days of their 18th birthday and fill out registration forms. Failure to do so is a felony punishable by up to five years in prison and a $10,000 fine.

Groups opposing compulsory registration contend it is an unnecessary peacetime intrusion that will save no time in getting men drafted if war should come, partly because young men are so mobile, and that it really represents the first step toward conscription.

The American Civil Liberties Union has said that trying to prosecute and jail the thousands of young men who refuse to register would prove as overwhelming and futile as enforcing the 1920s prohibition against selling alcoholic beverages.

The April 12 meeting at the Pentagon of President Reagan's Military Manpower Task Force focused not on those longstanding objections but on the political problems that prosecutions might generate. (Selective Service said yesterday that it has referred 225 people to the Justice Department for possible prosecution by local district attorneys--122 old cases and 103 new ones.)

When queried by The Post about his remark in the transcript about prosecuting non-registrants in the District of Columbia, Weinberger said he was contending that "if it were done here, you'd have the opposite of a quiet situation. There would be a great deal of public interest focused."

Asked what he meant by "current situations and all" in making recommendations to Justice, Weinberger said he was suggesting that the department might want "to think twice" about prosecuting in certain areas of the country, such as where there is high unemployment.

"Just in general there ought to be other considerations--other things should be considered," he said. "There could be quite a lot of problems in 500 or 600 suits." Weinberger said the anti-nuclear movement was not one of the problems he had in mind.

After being shown a copy of transcribed remarks from the meeting, Weinberger said the transcript was an unedited "first cut" that he had not classified secret but also had not authorized for public release.

In discussing how to prod 18-year-olds to register, White House counselor Meese said: "You could have a line on each of the applications: Have you registered for the draft? And if they put no, then you withhold their benefits. If they put yes, then you get a few that have done it fraudulently; you can kick them off their benefits and prosecute them."

Although there have been bills introduced in Congress to deny such federal benefits as college loans to non-registrants, no such legislation has advanced into law nor been formally advocated by the Reagan administration, according to Selective Service.