Walter F. Mondale today moved to bugle the Democrats home here by quoting a letter Ronald Reagan wrote to Richard M. Nixon in 1960 that likened John F. Kennedy's ideas to those of Karl Marx and Adolf Hitler.

The recently unearthed, three-page handwritten letter, sent to Republican presidential candidate Nixon just after the Democratic National Convention had nominated Kennedy for president, reads in part:

"One last thought, shouldn't someone tag Mr. Kennedy's bold new imaginative program with it's sic proper age? Under the tousled boyish haircut it is still old Karl Marx -- first launched a century ago. There is nothing new in the idea of a Govt. being Big Brother to us all. Hitler called his 'State Socialism' and way before him it was 'benevolent monarchy.' "

Mondale, hands and face shaking, told a rally at Youngstown State University here, "That's a big difference between the two of us. I believe that a president who cares, who leads -- just as Kennedy did -- can make and must make a difference in the lives of our country. That's not Karl Marx. That's not Adolf Hitler. That's America. That's America at its best."

Later in Chicago, Mondale said that Reagan has been going throughout the country this year claiming to be Kennedy's "best friend" and that the letter would "remind the people who Ronald Reagan really is . . . . Any adult who tries to compare Jack Kennedy to the ideas of Karl Marx and Adolf Hitler is not going to improve with age."

In Chicago, Mondale conducted a closed unity meeting with Mayor Harold Washington and Cook County Democratic Chairman Edward R. Vrdolyak, arch political rivals. Mondale said later that there is enough "harmony" among Chicago Democrats for him to carry Illinois.

He capped the day with a speech to the Urban League in Chicago that was interrupted three times by peristent hecklers, at least one of whom was a supporter of presidential candidate Lyndon LaRouche.

Mondale has been lampooning Reagan all fall for "political grave robbing" Democratic leaders of the past. Today he used the letter as a springboard to draw more starkly than ever the difference between the two parties on the fundamental question of government's role.

"I was reared in a tradition that says when people are in trouble, government is supposed to be there to give them a little chance, a little help," he told an audience of 1,500 in this economically depressed steel city of the industrial Midwest, a region where Mondale will be campaigning heavily in the final two weeks before Nov. 6.

Later, at a large rally under clear sky at the University of Michigan in Ann Arbor, Mondale told students that Kennedy's activist notion of government came from "the idealism of America."

At both stops, he was introduced with some stirring come-home-Democrats lines from one of his rivals for the nomination, Sen. Gary Hart (D-Colo.), who depicted the campaign as a choice between Reagan's appeals to "greed and self-interest" and Mondale's to "idealism . . . social justice . . . equality of opportunity."

Later, White House spokesman Larry Speakes confirmed that Reagan wrote the letter. He said the president "was pleasantly surprised to find the difference between Kennedy the candidate and Kennedy the president."

On arrival in Columbus, Ohio, today, Reagan said, "If you read the letter, you will find there is nothing wrong with it."

At the time he wrote it, Reagan was host of the television show "Death Valley Days" and active in a Democrats-for-Nixon political organization.

While Mondale turned his attention today to classic Democratic issues of education, the environment, civil and equal rights and tax fairness, he did not abandon his cut-and-slash treatment of Reagan's debate performance Sunday night.

Before both college audiences, he hit especially hard at Reagan's proposal to introduce a new generation of "Stars Wars" weapons, a subject of three Mondale television ads now airing nationally.

Mondale used "Stars Wars" both to raise fears of a ratcheting up of the arms race and to ridicule Reagan for not knowing the details of his own proposal for a space-based defense system.

In the Youngstown appearance, Mondale performed an unusual act of political contrition today, acknowledging that the Carter administration, in which he was vice president, had not done enough to keep the steel industry from going into a steep slide in the late 1970s. It was an issue Hart had used effectively against him to win the Ohio primary last spring.

"Let's admit that none of us has done what is needed for this region," Mondale said, promising in the first month of his administration to appoint Democratic vice-presidential nominee Geraldine A. Ferraro to head a special commission that would try to revive the steel industry.