The leaders of the United States and the Soviet Union talked business together for the first time in four years here today and quickly found themselves in dispute about the responsibility for spiraling military programs in both nations.

President Carter and Soviet President Leonid Brezhnev also disagreed, according to authoritative American sources, about the nature of the regional instability which has soured their relations in the past several years and which threatens a further growth of superpower tensions in Africa, the Middle East and Asia.

At the same time, Carter and Brezhnev were reported to be in remarkably close agreement on the overwhelming dangers of a mistake or miscalculation that could lead to an outbreak of nuclear war.

The firing in anger of even a single one of the many thousands of nuclear weapons in the hands of the superpowers could lead to "the final and ultimate catastrophe" for mankind, the Soviet leader was quoted as saying in his first summit meeting with Carter.

The U.S. president, agreeing in substance, spoke later in the day of the common efforts of the two nations to avoid "a nuclear conflict which some few might survive but which no side could win."

The signing of the second Strategic Arms Limitation Treaty (SALT II) to place curbs on their growing nuclear arsenals is the occasion that has brought the two men together at last.

Carter suggested in a toast made public tonight that the SALT agreement could provide "the basic framework" for the reduction of East-West military and political strains throughout the world. He did not say how this might be accomplished.

The first Carter-Brezhnev session, around a conference table at the U.S. Embassy, was a somewhat formal recitation of views on the current state of U.S. Soviet relations and the prospects for improvement. The first meeting ended about 35 minutes ahead of schedule after prepared statements by the two leaders.

An afternoon session to discuss and confirm sensitive agreements on SALT II and make a start toward SALT III ran 25 minutes longer than scheduled.

White House Press Secretary Jody Powell said later that all SALT II matters were resolved and that the treaty is ready for signing Monday.

Among the matters discussed by Carter and Brezhnev were the controversial $30 million MX missile recently authorized by Carter and the politically touchy matters of the SALT treaty's short-term protocol, verification measures and the Soviets' backfire bomber.

Brezhnev, in what seemed to be a half-joking reference to Carter's struggle for U.S. Senate ratification of SALT II, expressed "hope" (according to a Soviet spokesman) or "absolute confidence" (according to a U.S. version) that the Supreme Soviet will ratify the document without change.

Soviet officials hinted broadly that Senate amendments to the treaty will not be accepted, but there was no report that Brezhnev had made this point explicitly to Carter.

Brezhnev walked stiffly and slowly entering and leaving the day's meetings and departed to some extent from his previously prpared remarks and so occasion engaged in banter with Carter.

Soviet spokesman Leonid Zamyatin, asked at a press conference about Brezhnev's health, said the 72-year-old leader has "no complaints" about his health and dismissed reports to the contary as "nothing but speculations."

A Soviet journalist then asked Powell about Carter's political health.

"About the same," replied the White House official to general laughter.

Carter played host tonight to an intimate "working dinner" of roast beef and wine at the U.S. ambassador's residence for Brezhnev and the top three aides on each side. The guests, in addition to the two leaders, were Secretary of State Cyrus R. Vance, Defense Secretary Harold Brown and presidential assistant Zbigniew Brzezinski, and on the Soviet side Foreign Minister Andrei Gromyko, Defense Minister Dmitri Ustinov and Konstantin Chernenko, administrative chief of the Pollitburo.

Although the day's discussion exposed longstanding differences between the two nations, American officials took comfort that disagreements are being discussed candidly, if so far only in general terms.

Carter told Brezhnev, according to Powell's official account, that the United States seeks "clarification, conciliation and consultation" with the Soviets where differences exist.

Disagreement over the responsibility for the growth of military arsenals came to the surface in Brezhnev's opening statements, according to U.S. sources. The Soviet leader reportedly characterized his nation's programs as a reaction to large recent increases in U.S. military spending.

"We hear your speeches, Mr. President, but we see your massive increases in defense spending," an American participant quoted Brezhnev as saying to Carter.

The U.Ss. president, in turn, reportedly contested the Soviet view. He referred to large increases in Soviet defense spending over the past 15 years as measured by U.S. intelligence, and described the U.S. programs as a moderate and necessary response.

Due to human nature, Carter continued, each country tends to exaggerate the actions of the other. He added that the natural desire for secrecy can be counter-productive because it tends to build suspicions and may induce the development of "countermeasures" which may be unnecessary.

Brezhnev, at this point, reportedly interjected, "Off the record, Mr. President, we have read reports in the Washington papers that the United States had drafted a defense budget much higher than last year's."

U.S. official data released earlier this year reported a steady increase in Soviet military spending, adjusted for inflation.The data said that the Soviet Union has expanded its military establishment by about a million men since Brezhnev succeeded Nikita Krushchev as Soviet leader in 1964 and that more than 1,000 land-based intercontinental launchers and more than 900 submarine-based ballistic missile tubes have also been added.

Carter responded, according to the U.S. account: "Off the record, Mr. President, the Soviet Union has had a much larger increase than we have."

U.S. data show that Soviet Military expenditures, manpower and missile strength has been outpacing the United States in growth since Brezhnev succeeded Nikita Khrushchev as Soviet leader in 1964.

The U.S. defense budget has begun a major increase adjusted for inflation only in the last several years.

The problem of regional disputes which may involve superpowers also arose in the first presentation by Brezhnev. He stated the traditional Soviet position of "solidarity with the liberation struggles" and "struggles for independence and social progress" throughout the world. He repeated that position in the prepared toast for the working dinner with Carter tonight, adding that such struggles are falsely labeled at times as "Moscow's intrigues and plots."

Responding at the conference table, Carter said that struggles for independence and freedom inevitably occur, but it is critical that the two superpowers restrain themselves to avoid competition and conflict in such circumstances.

"We must restrict military intervention either directly or through third parties," Carter is quoted as having said. It is not clear whether he spelled out the names of the "third parties," which in the U.S. view include Cubans in Africa and now Vietnamese in Cambodia.

Substantive issues regarding strategic arms arose in the afternoon meeting, which was devoted largely to a restatement at the highest levels of the understandings and interpretations crafted in the long-running SALT II negotiations. The Americans evidently felt the need to repeat some of these agreements at the Carter-Brezhnev level to emphasize their importance to Washington.

According to the U.S. account, Breznev said he did not understand why Carter found it necessary to authorize a large new missile such as the MX at a time of arms control agreement. Moreover, the Soviet leader is reported to have warned that any variant of the proposed mobile missile that is not verifiable by "national technical means" such as spy satellites and radar would "place a mine" under the successor SALT III negotiations.

Carter did not respond directly to the question of why MX is being authorized now, U.S. sources said. However, he is said to have reminded Brezhnev that the United States has pledged that the MX will only be deployed in a way can be verified by "national technical means."

Carter is said to have informed Brezhnev officially that the short-term protocol covering some cruise missile issues is not a precedent for longer term agreements and reiterated that the protocol will expire on Dec. 31, 1981. This is a sensitive matter with SALT critics who favor full-scale deployment of ground-launched and seal-launched cruise missiles, particularly in Europe.

Carter repeated to Brezhnev key points of the negotiated understandings between the two sides limiting the encoding of missile testing data, or telemetry, and limiting the production and effective range of the Soviet backfire bomber.

In addition to the two leaders and the top aides who attended tonight's dinner, the uniformed chiefs of staff, ambassadors in one another's capitals, press secretaries and several other officials attended the first day of summit talks. With the exception of a single explanation by Gromyko, the only substantive talk across the conference table was by Carter and Brezhnev. CAPTION: Picture, Presidents Carter and Brezhnev wave as they depart from the U.S. Embassy after the first round of talks. UPI