The United States and Soviet Union reported progress at the White House yesterday toward concluding a new treaty to limit their strategic nuclear weapons, and scheduled an unusual Sunday morning session in drive for agreement.

Both Secretary of State Cyrus R. Vance and Soviet Foreign Minister Andrei A. Gromyko, after nearly four hours of discussions led by President Carter, told reporters that there had been "movement" in the negotiations.

The carefully measured phrases of the two foreign ministers and the comments of other officials point to the potential for a breakthrough toward the resolution of the final outstanding issues, rather than the reality of a breakthrough.

American officials were waiting expectantly to see if Gromyko will be able to bring definitive Soviet responses to new U.S. proposals to the State Department meeting of the two delegations, scheduled to begin at 9:30 this morning. It was unclear whether Gromyko would be able to obtain Politburo decisions on the tradeoffs being discussed in time for the State Department session.

If the Soviets accept the new American proposals as the basis for bridging the gap on the remaining issues, the drafting and technical work involved is likely to consume at least a month. Therefore, a final treaty in this optimistic timetable, would come just before or shortly after the U.S. congressional elections in early November.

Failure to reach basic agreement on a "package deal" involving the final sets of issues in the next day or two would require another set of high-level meetings possibly a trip by Vance and U.S. negotiating team to Moscow.

This would put back the timetable somewhat, but would still hold out the possibility of concluding a new treaty before the end of the year, a target date cited by Carter, Vance and other top officials.

A summit meeting between Carter and Soviet President Leonid I. Brezhnev for signing the treaty is likely late this year or early next year, in the view of increasingly optimistic administration officials.

Vance and Gromyko turned aside reporters' questions yesterday about a possible summit, but in both cases their answers were hedged. Vance said the matter had not come up "this morning," and Gromyko said he would not comment "for the time being."

The current round of bargaining, which is unusually intense, is the fourth set of high-level negotiations in five months on the new strategic arms limitation talks (SALT) treaty.

The quickened pace of negotiations and the positive statements from negotiators on both sides in recent days are signs that the final round may be at hand in the six years of bargaining for a treaty to limit the strategic offensive armaments of the two superpowers.

Yesterday's meeting was preceded by six hours of negotiations in New York Wednesday and Thursday between the two SALT teams headed by Vance and Gromyko, during which the Soviet side presented a package of proposals, which some U.S. sources described as relatively forthcoming, on the remaining issues.

At the outset of yesterday's session, Carter and Gromyko met for 15 minutes without their advisers in the Oval Office before joining the two delegations in the Cabinet room. Shortly after the larger session began, "Miss Lillian" Carter, the president's mother came into the room, was presented to Gromyko and the other Russians, and remained for five or 10 minutes of the discussion.

The Cabinet room talks began with Soviet-American relations and other international issues in which the superpowers have a major interest, and then turned to the main business of SALT. At the end of the general business session, Carter was host to Gromyko and Vance in a private luncheon to continue the discussion in the family quarters of the White House.

Accompanying Gromyko in the Cabinet room talks were Ambassador to the United States Anatoly Dobrynin and six other Soviet officials. Accompanying Carter and Vance were Vice President Mondale, Secretary of Defense Harold Brown, director Paul C. Warnke of the Arms Control and Disarmament Agency, Ambassador to the Soviet Union Malcolm Toon, presidential national security adviser Zbigniew Brzezinski, his deputy, David Aaron, Reginald Bartholomew of the National Security Council Staff and interpreter William Krimer.

Meeting reporters on the South Lawn before the luncheon, Vance said the two sides had "a good and constructive meeting." He added that "there was movement which I think both of us agree was constructive."

Gromyko, in turn, said through his interpreter: "Our talks have shown that this is a complicated issue, and the talks themselves are complicated. At the same time, I must say that some signs have appeared of a certain movement forward on some of the questions where we had previously either not reached agreement or had not reached full agreement."

The Soviet minister reiterated, as in a public statement in New York Thursday, that "the talks have now reached a stage where the solution to the questions depends on the sum total of other open issues, and they must therefore all be considered and resolved in one context."

The details of the package proposals of the two sides and the complex bargaining, which was described by informed sources as high-level horse-trading, were not made public. The issues still in contention, however, were known to include:

Exceptions for each side from a proposed ban on flight testing and deployment of "new types" of intercontinental ballistic missiles. Each side wishes exceptions to accommodate some planned additions to its nuclear arsenal while the Salt II treaty is in force, but the exceptions each proposed have differed.

Restrictions on the range and deployment of air-launched cruise missiles, under development by the United States.

Restrictions on the production, basing and effective range of the Soviet Backfire bomber, which the United States maintains is a strategic weapon but the Soviets say is not.

The duration of a treaty "protocol," which covers several of the most difficult issues, and the precise deadline for the small scale reductions in the Soviet missile force which are required by the previously agreed-to limits on the number of strategic nuclear reentry vehicles.

A statement of principles for negotiation of deeper cuts in nuclear arsenals in a future Salt III treaty.

The Soviet Union has proposed that Salt III include medium-range nuclear weapons, based in Europe, which are capable of reaching Soviet territory. These weapons, sometimes known as "gray-area" systems, are of great importance to European allies of the United States.

The "gray-area" weapons are among the topics to be discussed by adviser Brzezinski with top leaders of France, West Germany and Britain early this week, in a trip announced by the White House yesterday. Other topics for Brzezinski include the Camp David agreements and the situation in Lebanon, according to informed sources.