The United States and the Soviet Union were reported very close to final agreement on a new strategic arms limitation treaty (SALT) yesterday after a 40-minute meeting between Secretary of State Cyrus R. Vance and Soviet Ambassador Anatoliy F. Dobrynin.

Another meeting of the two officials for further discussion of the SALT pact is scheduled for Monday evening, the State Department announced.

Dobrynin, at yesterday morning's session at the State Department, is believed to have delivered the Soviet reply to Washington's proposals of March 29 for settlement of two remaining problems. U.S. sources said the Soviet Politburo apparently met last Thursday to make decisions on outstanding SALT-related questions.

The U.S. reaction to the message from Moscow is likely to be presented to the Soviet envoy by Vance at the Monday meeting.

After yesterday's session, Dobrynin told reporters that the two sides are getting "closer and closer . . . very close" to final agreement. He made no prediction of when the deal will be concluded and a summit meeting scheduled between President Carter and Soviet President Leonid I. Brezhnev.

In recent days, high U.S. officials have expressed growing confidence that, after many instances of unwarranted optimism over the past five years, SALT II is about to be completed.

Only two important issues are said to remain: unresolved details of the definition of the single "new type" of land-based intercontinental ballistic missile permitted under the treaty, and a clear-cut understanding of agreed limits to the encoding of missile testing information.

Two speeches by high officials, presidential assistant Zbigniew Brzezinski Wednesday and Secretary of Defense Harold Brown on Thursday, set out the Carter administration's case for the treaty.

Both placed heavy emphasis on the argument that SALT II would enhance U.S. national security, and both skirted any suggestion that the treaty would lead to a new era of Soviet-American amity.

The "SALT without detente" approach appears to be designed to appeal to conservative opinion in Congress and public opinion. The Choice of Brzezinski and Brown to make the opening case is a sign of administration concern about those with doubts that the United States is tough enough in deals with the Soviets.

A Radio Moscow report on the two speeches late Thursday welcomed them as evidence of a broad campaign by the Carter administration for SALT II. The radio report said it was "remarkable" that Brzezinski, who is often depicted as leader of an anti-Soviet tendency within the U.S. government, spoke out for the treaty.

Administration officials said plans for major speeches and other efforts to explain and promote the treaty are well advanced. Vance and Brzezinski have scheduled SALT speeches at the end of this month, and lower-ranking officials will be speaking here and on the road in coming weeks.

At the State Deparment Thursday, Vance appealed to the presidents of the television networks, in a private meeting, to give full coverage and as many "news specials" as possible to SALT. His message, according to aides, was that the treaty is a matter of such great complexity and historic importance that television is called upon to make extraordinary efforts. CAPTION: Picture, AMIR ABBAS HOVEYDA . . . death in a prison courtyard