Soviet Foreign Minister Eduard Shevardnadze yesterday presented to President Reagan a new arms-control proposal calling for cuts in the superpowers' strategic nuclear arsenals of 50 percent and cessation of work on Reagan's Strategic Defense Initiative, according to administration sources.

Shevardnadze, who met with Reagan for three hours in the White House, brought a long letter from Soviet leader Mikhail Gorbachev presenting his views of the summit meeting he is scheduled to hold with the president in Geneva Nov. 19-20. Neither U.S. nor Soviet officials, in separate news conferences, would give details of the letter or the new Soviet arms-control proposal, which will be presented to U.S. negotiators in Geneva next week.

The day's developments departed from the past pattern of U.S.-Soviet arms negotiations during the Reagan administration. For the first time the Soviets presented an extensive proposal -- in the past they have waited for the United States to take all significant initiatives. It was also unusual that the Soviets did not make their plan public and that the United States did not reject it out of hand.

The presentation of a detailed new Soviet proposal in Geneva next week will mark the beginning of the most intense phase of pre-summit diplomacy. Both countries now appear eager to demonstrate their willingness to negotiate, though the wariness on both sides was clearly evident yesterday.

Secretary of State George P. Shultz, who persistently refused to discuss details of what he called a Soviet "counterproposal" said, "we hope . . . it can lead to a process of genuine negotiation."

"The president welcomed what was put before him, as he did some of the other things that were said," Shultz told reporters at the White House. "The fullness of the proposal, of course, we'll have to judge when we see it in Geneva."

Administration sources who asked not to be identified said the Soviet proposal contains a 50 percent reduction from an overall total that remains uncertain. The Soviets would count all nuclear weapons, whether missile warheads, nuclear bombs aboard aircraft or weapons aboard U.S. submarines or warships, which they consider capable of striking the Soviet Union. The limits on nuclear weapons carried by bombers, in which the United States has a large advantage, have been resisted by several administrations.

In return the Soviets proposed a ban on all work on what they call "space-strike weapons," arms in space that are designed to attack objects in space or on Earth and arms on Earth designed to attack objects in space.

Such a ban was interpreted by administration sources as preventing research on the Strategic Defense Initiative, commonly called "Star Wars," even though Gorbachev in a Time magazine interview last month drew a distinction between "fundamental research" on SDI and activity which clearly should be banned.

Both Reagan and Shultz yesterday reiterated the president's commitment to the SDI project. The secretary of state said the president "insists on the importance of finding out whether, through the needed research and testing, it is possible to defend against ballistic missiles."

Reagan responded to shouted questions from reporters about SDI as he was seeing Shevardnadze to his car after lunch: "It is where it has always been. We are determined to go forward with the research."

Other elements of the Soviet proposal, as described by administration sources, include a ban on "new types" of strategic systems and a ban on deployment of nuclear weapons in areas of the world where they are not already deployed. The latter provision would evidently halt the proposed deployment of U.S. ground-launched cruise missiles in the Netherlands.

The Soviet proposal was described as applying only to U.S. and Soviet strategic arms and not to British and French missiles.

U.S. specialists said they considered some aspects of the Soviet proposal to be disappointing but much depends on the specific details that were not revealed by Shevardnadze and are due to be offered at Geneva next week.

The mood of the meeting yesterday was described as both businesslike and friendly. But Reagan took one jab at his Soviet visitor. After Shevardnadze had said that the details of the new proposal would be presented in Geneva, Reagan reportedly replied that he would prefer that to "reading about it in Tass," the Soviet news agency.

The meeting began at 10 a.m. and Shultz said Reagan "presented a comprehensive view of his thoughts about the upcoming meeting in Geneva, and then Mr. Shevardnadze gave the president a lengthy letter from General Secretary Gorbachev."

Shultz and other officials indicated that they thought that the letter, which was in Russian, would give details of the arms-control proposal which Shevardnadze described verbally in general terms to Reagan. But when the letter was translated later, officials said its contents were even more general than the foreign minister's explanation and cast no new light on what is to be proposed by the Soviets next week.

The president, seeing Shevardnadze to his car after two hours of discussions and a hour-long lunch, declined to go into the contents of the meeting but said, "It's always progress when you talk to each other and we talked to each other." Shevardnadze met later in the day with Shultz for additional discussions and then was dinner guest, with his wife, Nanuli, at Shultz's home. U.S. officials said last night that the two foreign ministers had completed their discussions.

Following a White House news briefing by Shultz in the early afternoon, Soviet Foreign Ministry spokesman Vladimir Lomeiko gave a news conference at the National Press Club at which he described the Soviet proposals as "important" but declined to give any details.

The backdrop for the unusual Soviet news conference was flags of the United States and the National Press Club. Word that the Soviets had scheduled a news meeting drew well over 100 journalists to a room that was designed to hold about half that number.

Lomeiko justified the secrecy about the new Soviet proposal by describing it as part of "a personal letter" from the Soviet leader to the U.S. leader, and said it would be "unethical" to disclose its contents. Reminded that Soviet arms initiatives often had been made public before they were presented to U.S. negotiators in the past, Lomeiko responded, "We're damned if we do, and damned if we don't."

Shultz welcomed the Soviet secrecy, saying, "We believe that the chances of getting somewhere in arms control are maximized if we don't have a lot of public things to say about it . . . ."

Shultz said that Reagan and Shevardnadze agreed on the "general structure" of the summit meeting, which will include discussion of various regional conflicts and bilateral issues as well as arms control.

Regarding human rights issues, which the Soviets consider an internal matter, Shultz said, "You can be certain that the president, as he did today, will always bring up the subject of human rights and express the importance which we attach to it."