The United States and the Soviet Union yesterday announced an "agreement in principle" to conclude a treaty to eliminate medium-range and shorter-range nuclear missiles, a joint commitment to an "intensive effort" to negotiate 50 percent cuts in their strategic offensive arsenals and a decision to hold a summit meeting here this fall.

President Reagan announced what he called this "notable progress" at a tumultuous White House briefing early yesterday, marking a decisive step toward the first U.S.-Soviet arms control agreement since 1979.

Reagan praised Secretary of State George P. Shultz and Soviet Foreign Minister Eduard Shevardnadze for "outstanding efforts" in their three days of intensive negotiations that saw an unusually cooperative attitude between officials of the two nuclear powers and a number of Soviet concessions across a broad range of arms control issues.

Shevardnadze, in a news conference at the Soviet Embassy, called yesterday's agreements "the first major step toward a nuclear-free world" and said his meeting in Washington marks "the beginning of a new period . . . a reflection of the beginning of detente."

Shultz, who declared that "things have changed tremendously in the relationship between the United States and the Soviet Union," is to fly to Moscow in the second half of October to work out final details of the intermediate-range nuclear forces (INF) treaty and to prepare for the trip by Soviet leader Mikhail Gorbachev to the United States, probably in late November.

Officials and presidential intimates said the most likely time, if Gorbachev agrees, is Nov. 15-21, the week before Thanksgiving. They said that in addition to a Washington official visit, Reagan would invite the Soviet leader to tour the United States and visit him at his ranch northwest of Santa Barbara if Gorbachev expresses an interest in such a tour.

The INF accord agreed to in principle would be the first U.S.-Soviet treaty actually to reduce the number of offensive weapons rather than to cap their burgeoning growth. And, for the first time, it would eliminate an entire class of nuclear weapons. But the missiles to be eliminated represent only about 5 percent of the vast U.S. and Soviet nuclear arsenals, estimated at 50,000 weapons all told.

Shultz, Shevardnadze and other officials said the breakthrough that assured "agreement in principle" concerned the contentious issue of U.S. nuclear warheads for West German Pershing IA missiles. The Soviets had demanded assurances that the warheads will be removed and destroyed; the United States insisted that the weapons are part of a longstanding cooperative relationship with the West German ally and hence beyond the scope of the U.S.-Soviet treaty.

The solution was suggested by U.S. arms adviser Paul H. Nitze in "working group" discussions with Soviet negotiators Wednesday, cabled to Bonn overnight and approved by Shultz and Shevardnadze in a sometimes difficult discussion lasting more than an hour Thursday morning.

While continuing to insist on the current immunity of the Pershing IA warheads from consideration in superpower discussion, the U.S. side agreed that once the West German delivery systems, or missiles, are destroyed, as recently promised by Chancellor Helmut Kohl, the U.S. warheads will no longer be part of a special cooperative arrangement and "therefore subjected to the same elimination procedure and timeframe for final elimination" as all other weapons covered by the INF treaty.

Shevardnadze called this "a wise and intelligent solution to this very sensitive problems." In a highly unusual gesture of acceptance of the U.S. relationship with its West German ally, Shevardnadze said the Soviet Union in accepting this arrangement "sought to take into account to the maximum possible degree the alliance interests of the United States and also of the Federal Republic of Germany; {and} naturally, also take into account the needs of the Soviet Union."

Despite the developing mood of optimism, officials pointed out that the two nations remain at cross purposes in almost every area of foreign and military policy and many areas of internal policy. Reagan, in his announcement, said the United States and Soviet Union continue to have "serious differences in many areas."

In the din of the White House press room a reporter shouted to Reagan, "What about the 'evil empire?' " a phrase the president applied to the Soviet Union in a March 8, 1983, address at the National Association of Evangelicals but which he has not uttered in public since meeting Gorbachev for the first time in November 1985 in Geneva. "Oh, I don't think it's still lily white," Reagan replied with a smile.

A sign of the determination to surmount obstacles was shown in the careful handling by both sides of the wounding of a U.S. sergeant by a Soviet soldier in East Germany Thursday. Shultz, who termed the shooting of the sergeant on a military liaison patrol "unacceptable behavior," protested it to Shevardnadze during their talks Thursday.

After obtaining information from Moscow, Shevardnadze publicly apologized for the shooting during his news conference yesterday, though he also said that both soldiers had been at fault. Reagan refused reporters' calls for comment on the incident, referring questions to Shultz. An administration official said the United States is not trying to "exploit" the shooting.

Reagan, whose foreign policy and domestic political standing in his final 16 months in office may be deeply affected by a changed U.S.-Soviet relationship, displayed an unusually intense personal interest in this week's negotiations. In sharp contrast to the passivity the president has often displayed during arms negotiations in which he was not directly involved, "He has been riveted all week on the talks" and "repeatedly asked for briefings," according to an aide.

A White House official said Reagan was particularly pleased by the INF treaty progress because his original 1982 proposal for a "zero option" to eliminate all INF missiles from Europe was "scoffed at" when it was first presented. Asked by a reporter if he was in too much of a hurry to rush into a summit meeting to sign the INF treaty, Reagan said, "I don't know of anything in my life I waited over six years for."

Nancy Reagan, who is known to be an advocate of U.S.-Soviet amity in the White House, was quoted by an aide as saying of the prospective agreement and summit, "It sounds very encouraging and that makes me happy."

Administration officials said that the mood of optimism will be reflected in Reagan speeches and that the president plans to "campaign hard" for ratification of the INF treaty once it is signed. Today, Reagan is expected to hail the week's accomplishments in his weekly radio address.

Aides said that portions of the speech Reagan will give to the U.N. General Assembly on Monday have been rewritten to reflect this week's developments and "smooth out some of the rough edges" in which the president was particularly critical of Moscow.

But Reagan is still likely to voice criticism, at least indirectly, of Soviet behavior in Afghanistan. Shultz said he and Shevardnadze had a thorough discussion of the Afghanistan issue but made no progress in resolving it or in shortening the timetable which has been offered by Moscow for withdrawal of its forces.

On human rights issues, Shultz said "our principal progress" was in establishing regular procedures to deal with the cases of would-be Soviet emigrants, dissidents and others of interest to the United States. "We see very worthwhile discussions and movement in terms of behavior in the human rights area," he said.

In bilateral issues, U.S. officials reported agreement on a lengthy "work program" ranging from talks on transportation and oceans agreements to new negotiations about Soviet grain purchases from the United States.

The new arms control developments, as listed by U.S. officials, included:INF: The Soviets agreed tentatively to a one-year timetable for elimination of short-range nuclear missiles and a three-year timetable for elimination of medium-range missiles, as proposed by the United States. The two sides also cleared up confusion and potential disagreement about the destruction of nuclear material in warheads covered by the agreement. Space weapons: The Soviets abandoned their previous demand that the United States agree to tough, highly detailed constraints on the U.S. Strategic Defense Initiative (SDI). Instead, Moscow agreed to settle for a U.S. promise to abide by the original interpretation of the 1972 Antiballistic Missile (ABM) Treaty for a 10-year period, without spelling out any more detailed limitations. Strategic arms: The Soviets agreed for the first time to reduce by half the number of warheads on their largest land-based missiles, the SS18, as part of a possible overall accord. They revived a previous proposal that no more than 60 percent of U.S. and Soviet nuclear warheads be concentrated in any one leg of the strategic triad of land-based missiles, bombers, and submarines. The Soviets also agreed to accept permanent limits on the overall capability, or throw weight, of their land- and sea-based missile force. Nuclear testing: The Soviets accepted a U.S. agenda for negotiations to limit nuclear testing that will begin by Dec. 1. The two sides will start by improving methods to verify unratified 1974 and 1976 testing treaties, and only later move to consider stricter limits and an eventual ban on all nuclear tests. Chemical weapons: The Soviets offered for the first time to exchange detailed information on the composition of their chemical weapons stockpile.

Staff writer R. Jeffrey Smith contributed to this report.