Vice President Bush sought today to prove that Walter F. Mondale suggested that American Marines "died in shame" in Lebanon, producing statements in which Mondale said President Reagan's policies had "humiliated" the United States in the Middle East.

Bush, who called a news conference to defend his debate charge against claims by the Democratic presidential nominee that it was "libelous," referred reporters to the American Heritage Dictionary, which defines humiliation as "degradation, disgrace and shame."

"That's what I base my comment on. I go back to the definitions in the dictionary," Bush said.

Bush has been faced here with questions not only about that remark but also about a 1980 interview in the Los Angeles Times in which he was quoted as saying a nuclear war was winnable.

Bush denied in last Thursday's debate with Democratic vice-presidential nominee Geraldine A. Ferraro that he made the statement about nuclear war, but the Times reprinted it this week and local television stations replayed the Times' tape of Bush explaining in detail "the way you can have a winner," as he put it.

Regarding his "died in shame" remark, Bush today produced no quotes from Mondale or Ferraro saying the Marines died "in shame." Instead, he read aloud five critiques they made of U.S. policy in Lebanon after the bombing of the U.S. Embassy annex in east Beirut last month.

"Once again we're humiliated in this region," Mondale was quoted as saying on Sept. 24.

"More than 250 young men died in a mission without a purpose and for a policy that's never been explained," Ferraro was quoted as saying Sept. 20. She was referring to the 1983 bombing of the Marine compound, which she linked to the embassy bombing by saying there were security lapses at both.

"They can demand an apology every day," Bush said. "But the fact of the matter is that accusing young men of dying without a purpose and for no purpose is in the lexicon of the American people a shame."

Asked if he was equating criticism of Reagan's foreign policy with criticism of the Marines, Bush responded: "Nobody has to say it's a tremendous 100,000 percent success. . . . . I hope I'm not so defensive that any criticism of the policy I would equate with humiliation."

Bush was reminded by reporters that he said last month that America "suffered humiliation" in Iran during the hostage crisis under former President Carter. Asked if this suggests that eight U.S. servicemen killed in a failed rescue mission in 1980 "died in shame," he said: "I haven't thought about the people who died there, and I hope that nobody would think that they died in shame."

But Bush distinguished between the Iranian crisis and the Lebanon bombing, saying the United States was contending with a foreign government in Iran and with random terror in Lebanon.

Bush's 1980 remarks on nuclear war came in response to a question from Los Angeles Times reporter Robert Scheer about whether the nuclear arms race is out of control. He responded: "If you believe there is no such thing as a winner in a nuclear exchange, that argument makes a little sense. I don't believe that."

"How do you win a nuclear exchange?" Scheer asked.

"You have a survivability of command and control, a survivability of industrial potential, protection of a percentage of your citizens and you have a capability that inflicts more damage on the opposition than it can inflict on you," Bush said on the tape. "That's the way you have a winner, and the Soviets' planning is based on the ugly concept of a winner in a nuclear exchange."

Bush's press secretary, Peter Teeley, said the vice president was referring to Soviet planning for a nuclear war and does not believe nuclear war is winnable.