IT is a moral conundrum worthy of Shakespeare: publish or someone might perish. That, in theory at least, is the dilemma facing two prominent American newspapers, the New York Times and the Washington Post, as they grapple with whether to print the 35,000-word Unabomber manifesto. If they do, the elusive terrorist, whom authorities suspect of killing three people with letter bombs since 1978, says he won't strike again. He has set the end of September as a deadline. Though it is a quandary confronting the two papers, it is also quietly stirring an ethical debate across the entire industry. It raises fundamental questions about the role and mission of the press in a free society. Such threats can compromise a paper's independence, turn it into a pawn in a game of cat and mouse, and set a deadly precedent. At the same time, it creates the opportunity to save lives. Some argue saving lives should take precedence over lofty ideals of journalistic integrity. Others contend that any capitulation would inspire copycats and, ultimately, threaten more lives. ''We view it primarily as a public safety issue, not as a journalistic decision,'' says Bo Jones, president and general manager of the Washington Post. ''At this point, we haven't decided whether to run it or not.'' The Times declined to comment, deferring to a statement made by publisher Arthur Sulzberger, Jr. on Aug. 2, when both papers ran excerpts from the manifesto, along with news stories about the FBI's decision to distribute it to dozens of college professors in hopes they would recognize a former student in the writing. The Unabomber is demanding that all 35,000 words be published. ''As I've said before, the demand that the Unabomber have access to our pages for three years is especially troubling,'' Mr. Sulzberger's statement read, referring to the Unabomber's demand that he have access to the Times' pages for followup comments. ''There's no easy way to open negotiations with this person and for the moment we're stymied.'' One question being raised is how much newspapers should cooperate with law enforcement authorities. Several analysts see in Sulzberger's statement an effort to draw out the Unabomber, and suggest the Times may be working with the FBI. They see such a move, if true, compromising its independence. Others see a genuine effort to start a dialogue that could preserve the paper's integrity and at the same time accommodate the Unabomber. Consulting with FBI Mr. Jones of the Post says they will consult with law enforcement before they make their decision, but it will clearly be the Post's decision. The FBI says the same is true about the Times. ''The decision to publish or not publish is solely up to the New York Times and the Washington Post,'' says George Grotz, spokesman for the FBI task force that is tracking the Unabomber But others insist that newspapers should not even be talking with law enforcement. ''You don't cooperate with the police, ever,'' says Stephen Isaacs, a professor of ethics at the Columbia School of Journalism. ''It's not our job to catch a serial killer; it's our job to report what we see to be news, period.'' Others who subscribe to the ''don't publish'' school are concerned about setting a precedent by negotiating with terrorists, which could inspire others to make similar threats. ''What happens when you get a call from a guy in his basement who says he's going to blow up his wife and kids unless he gets the Op-Ed [opinion] page?'' asks Mark Jurkowitz, the Ombudsman for the Boston Globe, who is also worried about a paper compromising its independence. ''I just don't see how you get into this process without being a pawn in a game between the Unabomber and the police,'' he says. Safety vs. independence ''That's always going to be the relationship with all news sources: You use them, they use you, that's part of the game,'' counters an editor at a major paper, which at one time published a note from the Unabomber. ''You're talking about helping to catch a serial killer here.'' The editor, who requested anonymity, said a paper has to weigh the public's safety against journalistic independence. ''If we can prevent him from killing one more person the whole thing becomes worthwhile,'' says Bob Guccione, editor in chief and publisher of Penthouse Magazine, who has offered to print the manuscript in full. But the Unabomber has declined, saying Penthouse is an entertainment magazine that runs counter to his purpose. ''If he was just interested in getting published,he'd have accepted Penthouse's offer, but he wants a better address,'' says Everette Dennis, the executive director of the Freedom Forum Media Center at Columbia University. Mr. Dennis contends the credibility of the media suffers when it turns over its pages or airwaves to terrorists' demands. But John Dillin, managing editor of The Christian Science Monitor, believes that when lives are at stake you have to reconsider ''textbook'' ideas about independence. ''In a case like this, I think one has to act based on your highest sense of what's right,'' he says. ''It's not an easy question.''