President Reagan and Soviet leader Mikhail Gorbachev exchanged simultaneously televised New Year's messages today and wished each other's people "a year of peace."

Both leaders cushioned deep differences between the two governments with words of optimism that echoed their joint statement issued at the conclusion of the Geneva summit on Nov. 21.

"Our duty to all mankind is to offer it a safe prospect of peace, a prospect of entering the third millennium without fear," Gorbachev said.

Reagan, calling the New Year "a time for reflection and for hope," said, "Let us look forward to a future of 'chistoye nyebo' for all mankind." The Russian words mean "clear skies."

Despite these hopeful words, both Reagan and Gorbachev took the opportunity to politely make their opposing cases on the U.S. Strategic Defense Initiative (SDI), often called "Star Wars," which has been a persistent sticking point in arms control negotiations between the superpowers.

Observing that the Soviet Union as well as the United States was engaged in research on missile defense, Reagan said, "If these technologies become a reality, it is my dream . . . to one day free us all from the threat of nuclear destruction."

Without directly mentioning SDI, Gorbachev said: "It is a reality of today's world that it is senseless to seek greater security for oneself through new types of weapons. At present, every new step in the arms race increases the danger and the risk for both sides, and for all humankind."

White House officials said before the messages were delivered that the event itself was more important than what either leader said. It was the first time U.S. and Soviet leaders had exchanged messages that were simultaneously televised.

Richard M. Nixon, in 1972, was the last president to address the Soviets on television. Soviet leader Leonid Brezhnev spoke to Americans on television the following year.

The Reagan administration had sought for nearly a year without success to obtain Soviet permission for the president to address the Soviet people on television. Officials said they were surprised when Anatoliy Dobrynin, the Soviet ambassador to the United States, approached Secretary of State George P. Shultz on Dec. 20 and asked if the United States was still interested in this proposal. Shultz said "yes," and the Soviets informed the United States on Dec. 24 that they had agreed to the request.

Reagan's five-minute message was taped last Saturday in the Century Plaza Hotel in Los Angeles and broadcast today at 9 p.m. in Moscow over a popular news program. At the same time, 10 a.m. in warm and sunny Palm Springs (1 p.m. EST), Reagan was watching Gorbachev deliver his seven-minute speech.

The president, dressed in golfing clothes, watched Gorbachev's address in the "room of memories" at the estate of publishing magnate Walter Annenberg, where Reagan is spending his vacation.

"I welcome his message as a continuation of our discussions in Geneva," Reagan said of Gorbachev's speech. "Let us hope that these words will be the foundation for making 1986 the year of peace our peoples deserve."

A White House official said that Gorbachev's speech was "constructive" both in tone and content.

In his message Reagan recalled the "good beginning" of the Geneva summit, where he and Gorbachev talked "frankly and seriously about the most important issues of our time: reducing the massive nuclear arsenals on both sides, resolving regional conflicts, ensuring respect for human rights . . . . "

Reagan said that both leaders agreed on the need to reduce nuclear arsenals and that U.S.-Soviet negotiators would attempt to reach new agreements curbing both intercontinental and intermediate-range nuclear weapons when they return to Geneva this month.

"And it's my hope that one day we will be able to eliminate these weapons altogether and rely increasingly for our security on defense systems that threaten no one," Reagan said in a plea for his missile defense plan.

The president also made mildly worded appeals for resolving human rights issues and regional conflicts, although he did not single out the Soviet occupation of Afghanistan, which he criticized in strong language last week.

Today the president called for "finding peaceful settlements to armed conflicts which cause so much human suffering in many parts of the world."

On human rights, Reagan said that "progress in resolving humanitarian issues in a spirit of cooperation would go a long way to making 1986 a better year for all of us."

In contrast to his pointed statements on Afghanistan, the president has adopted a strategy of "quiet diplomacy" on human rights issues, believing that the Soviets are more likely to make concessions on Jewish emigration and other issues if not publicly pressured.

U.S. officials point to recent Soviet actions allowing separated U.S.-Soviet families to be united as a small but positive indication of the merits of this approach.

Gorbachev said that one of the main results of the Geneva meeting "is that, as leaders and as human beings, we were able to take the first steps toward overcoming mistrust and to activate the factor of confidence. The gap dividing us is still wide, to bridge it will not be easy, but we saw in Geneva that it can be done."

Gorbachev asserted that "our common quest for peace" has its roots in past U.S.-Soviet cooperation beginning in World War II.

"We cherish the idea of peace, having suffered for it," Gorbachev said. "Together with the pain of unhealing wounds and the agony of irretrievable losses, it has become part and parcel of our flesh and blood. In our country there is not a single family or a single home that has not kept alive the memory of their kith and kin who perished in the flames of war -- the war in which the Soviet and American people were allies and fought side by side."