The United States and the Soviet Union made a guardedly promising start last night on a decisive phase of nuclear arms negotiations, signaling each other that a failure is certain to do great damage to their total relationship.

After 6 1/2 hours of morning and evening talks in the Kremlin, the equally wary negotiators would tell reporters only that they were encouraged by the seriousness displayed on both sides.An American spokesman last night stressed that "we are in negotiations" to signify that the delegations are not simply making posturing statements at each other.

As an indication of purpose, the delegations agreed to use the maximum time available in the present schedule of Secretary of State Cyrus Vance by projecting negotiations to run through Saturday afternoon, beyond the Thursday and Friday meetings orginally announced.

At the end of the initial sessions the American spokesman, relaying Vance's deliberately low-key diplomatic terminology to avoid arousing expectations that might collapse in another rebound against the Carter administration, said Vance regarded the first day's results as "useful" and the atmosphere as "good."

Between the day's two meetings, Soviet Foreign Minister Andrei Gromyko, at a luncheon honoring Vance, said solemnly: "I do think that I would be very close to the truth if I were to say that the responsibilities today upon him [Vance] and upon the Soviet Union might be greater today than they were during his previous visit to this country."

Gromyko added that he knew "we can all draw conclusions" about what he was referring to. He said he thought it best not to amplify that remark - which brought laughter from the audience of diplomats.

Gromyko was referring to the disastrous encounter 13 months ago in the Kremlin when the new, brash, untested Carter administration stunned the Soviet Union by calling for a drastic change in the arms control negotiating pattern.

The United States said its objective was to leapfrog the previous approach by moving swiftly to "deep cuts" in nuclear arsenals.

In an angry public crossfire the Soviet Union rejected out of hand all the American proposals, charging the United States with seeking "unilateral advantage." Carter fired back that the United States was determined to "hang tough."

It has taken the intervening months to thaw that frigid impasse and to bring the strategic arms limitation talks (SALT) to its present stage, within range of an agreement this year.

At yesterday's lunch, Vance, replying to Gromyko said, "We share the hopes and aspirations" that Gromyko expressed, adding "We have just started our work. We have just gone around the first lap of the track and I hope that before we conclude that it will then be a successful visit."

Soviet President Leonid Brezhnev did not participate in yesterday's meetings but is expected to be present at a later stage. For the first time in these formal Kremlin meetings on SALT, however, a leading Soviet general joined the diplomats. He was Gen. Nikolai Ogarkov, first deputy minister of defense and chief of the general staff.

Like U.S. Lt. Gen. Edward Rowny, who last year became the first general to sit in on these meetings, Ogarkov in the past has been on his country's delegation at the regular SALT negotiations. Rowny represents the American Joint Chiefs of Staff on the SALT talks in Geneva.

Among other things, the presence of the generals also underscores the technical nature of the nuclear bargaining. Although the decisions made at the level of meetings now under-way here are essentially diplomatic and political, they deal with nuclear hardware of increasing complexity.

There was a marked contrast in the atmosphere in the conference chamber yesterday, when reporters and photographers were present, compared to the first Kremlin meeting with the Carter administration in March 1977.

Thirteen months ago, the neophyte U.S. delegation charged onto the scene, as many observers saw it, "like gangbusters," just as the Soviet Union was bristling at the initial plunge by the Carter administration into its human rights demands, which the Kremlin regarded as gross interference into its domestic affairs.

The United States later toned down its human rights challenge of the Soviet Union, shifting the campaign to quieter diplomacy.

The human rights issue was not raised by Vance yesterday, although not far from the Kremlin it reappeared in front of the U.S. Embassy. There the distraught Soviet wife of a University of Virginia professor, who has been prevented by Soviet authorities from emigrating to join her husband, protested her treatment and was forcibly removed by Soviet police.

Yesterday's first meeting of the American and Soviet delegations in the Kremlin was indeed, in the diplomatic cliche, "businesslike." It was in the style of two boards of directors facing a momentous decisions, very uncertain whether they could agree on it and making little attempt to conceal their uncertainty.

Asked whether he expected progress in this round of meetings, Gromyko warily replied, "We have hope for hope."

Never too venturesome with humor, Gromyko lightly teased Paul Warnke, U.S. Arms Control Agency director and chief SALT negotiator, for having "a blank pad" in front of him instead of "the proposals."

Soviet television in portraying the opening of the meeting avoided any characterization of what was happening but film that showed Gromyko and Vance smiling and chatting amiably along with advisers.

There was also however, a protective countertheme being circulated by Soviet officials and newsmen who talked with American and other foreign reporters. They expressed regret and puzzlement that Vance, addressing the Central Treaty Organization ministerial meeting in London Tuesday reiterated portions of a stern speech on defense given by President Carter at Wake Forest University last month.

In it, Vance noted in London, Carter said, "We shall seek the cooperation of the Soviet Union and other nations in reducing areas of tension," but "we will match, together with our allies and friends, any threatening power through a combination of military forces, political efforts and economic progress."

The unofficial Soviet criticism of the timing and reiteration of the Carter warning on the eve of the talks here, however, U.S. sources said, was not carried into the Kremlin talks.

This also indicated the Soviet Union wanted to concentrate on negotiations not arguments. Vance began his remarks with a general review of U.S. Soviet relations, spokesman Hodding Carter III reported, but the later discussion was squarely on SALT with all other subjects deferred for the time being.