PALM SPRINGS, CALIF., JAN. 1 -- President Reagan and Soviet leader Mikhail Gorbachev today exchanged televised New Year's messages to the Soviet and American people calling for completion in 1988 of an accord that would make deep cuts in the strategic nuclear arsenals of the rival superpowers.

The five-minute messages celebrated improvement in U.S.-Soviet relations and the Intermediate-Range Nuclear Forces treaty signed last month at the Washington summit. But Reagan also made diplomatic references to persistent U.S.-Soviet differences on human rights, regional conflicts such as that in Afghanistan and the Strategic Defense Initiative.

"In some instances, regimes backed by foreign military power are oppressing their own peoples, giving rise to popular resistance and the spread of fighting beyond their borders," Reagan said. "Too many mothers, including Soviet mothers, have wept over the graves of their fallen sons. True peace means not only preventing a big war but ending smaller ones as well."

The president then praised the courage of the Soviet people during World War II and said, "Let us consecrate this year to showing not courage for war but courage for peace."

Gorbachev's conciliatory message referred only obliquely to U.S.-Soviet differences and not at all to SDI, Reagan's "Star Wars" missile-defense plan opposed by the Soviets.

But the Soviet leader did try to answer concerns that the INF Treaty eliminating medium- and shorter-range nuclear weapons would leave the Soviets with an overwhelming conventional military advantage in Europe.

"We would like without delay to address the problem of cutting back drastically conventional forces and arms in Europe," he said. "We are ready for interaction in resolving other problems including regional ones."

Gorbachev called the INF Treaty "the first step along the path of reducing nuclear arms" and said it "has brought our two peoples closer together. Reagan said the treaty is "just a beginning" and urged completion of an agreement to halve superpower strategic nuclear arsenals.

"Perhaps we can have a treaty ready to sign by our meeting in spring," Reagan said, referring to the summit that he and Gorbachev have agreed to hold in Moscow in the next six months. "The world prays that we will. We on the American side are determined to try."

Saying he holds a "vision of a world safe from war," the president then put in a plug for antimissile defense systems, an issue often a sticking point in U.S.-Soviet negotiations.

"Today, both America and the Soviet Union have an opportunity to develop a defensive shield against ballistic missiles, a defensive shield that will threaten no one," Reagan said. "For the sake of a safer peace, I am committed to pursuing the possibility that technology offers."

Reagan's open advocacy of SDI and human rights, "including freedoms of speech, press, worship and travel," was a measure of the evolution in U.S.-Soviet relations since Reagan and Gorbachev exchanged largely platitudinous New Year's messages two years ago.

Last year, the Soviets would not permit a televised exchange of messages, saying the state of U.S.-Soviet relations did not warrant it. Soviet Foreign Ministry spokesman Gennadi Gerasimov said in Moscow a year ago, "We have no basis for the exchange of such New Year's messages . . . . Why should we create any illusions about our relations?"

This year, the Soviets were so cooperative that they readily accepted a White House request to move the timing of videotaped messages forward an hour to avoid conflict with U.S. televising of the Tournament of Roses Parade.

In his message today, Gorbachev said political leaders of both superpowers must make progress toward peace by taking advantage of the "enormous stock of good will" that exists between the Soviet and American peoples.

"If they could only do that, what is but a dream today would come true -- a lasting peace, an end to the arms race, wider-ranging trade, cooperation in combating hunger, disease and environmental problems and progress in ensuring human rights and resolving other humanitarian issues," Gorbachev said.

The Soviet leader predicted that major changes would continue to occur in his country and accelerate international cooperation.

"There will be profound changes in our country along the lines of continued perestroika, democratization and radical economic reform," he said.

The leaders' messages were telecast live at 11 a.m. (EST) by Cable News Network and at 11:45 a.m. by ABC. NBC showed the messages at 1:18 p.m. (EDT) between the conclusion of the Rose parade and the beginning of the Fiesta Bowl football game.

Only CBS balked at repeated White House requests to carry the Gorbachev message at or near the same time that Reagan's message was being viewed in the Soviet Union. CBS used excerpts of the two speeches in regular news broadcasts.

Staff researcher Michelle Hall contributed to this report.