Soviet Foreign Minister Andrei A. Gromyko cast a glow of optimism over the prospects for improved American-Soviet relations after a three-hour meeting yesterday with President Carter.

This first encounter between Carter and a senior member of the Soviet hierarchy was significant in diplomatic atmospherics, even though no tangible results were evident.

The import was in the ambience of the meeting, in what was the unsaid as much as what was said. Gromyko, a histrionic artist in registering gloom when the Kremlin chooses to display it, was affably projecting hopefulness yesterday, to dispel the severe chill between Moscow and Washington that pervaded the early months of the Carter administration. Gone were the sharp barbs about the Center human rights campaign or the charges that the U.S. administration seeks "unilateral advantage" in nuclear arms control.

Instead, Gromyko, unusually voluble and affable to reporters, said "the Soviet leadership" conveyed to President Carter its desire to maintain and expand "good relations" with the United States.

A meeting between Soviet leader Leonid I. Brezhnev and Carter, Gromyko said, "was within our field of vision" in the White House talks, although that was not discussed "in detail."

Gromyko, virtually acting as the spokesman for both sides, with Secretary of State Cyrus R. Vance beside him saying very little, said Carter expressed his own hopes for improved U.S.-Soviet relations. Gromyko said Carter told him that since his election, it has been his desire "to maintain a good relationship with the Soviet Union and that is his view today, and that is the policy that he will go on pursuing."

"Of course," Gromyko said bluntly, "both sides agreed that this is but political algebra which so far still has to be translated into the language of practical politics."

This includes, Gromyko stressed, "so 'early' a problem as that of concluding a new [nuclear] strategic arms limitation accord." Then he unnecessarily cautioned reporters, "Please take the word 'easy' in quotation marks."

So far as the Soviet Union is concerned Gromyko said, it is confident that "we will reach a successful conclusion" in the strategic arms limitation talks (SALT).

Vance said "we share the same objective," but the emphasized, and Gromyko agreed, that "important questions" remain unsolved.

Gromyko declined to state to reporters at this time if the Soviet Union intends to declare that it will honor the arms ceilings in the existing American-Soviet nuclear accord which expires on Oct. 3. "So far," Gromyko told questioners coyly, "the first agreement is still in effect."

Vance, however, has told Congress that the United States and the Soviet Union each plan to issue what Vance called "a unilateral policy declaration" to respect existing arms ceilings set in 1972.

By avoiding a formal agreement to maintain the arms limitations in the expiring accord, the Carter administration hopes to avoid a congressional debate while negotiations for a new nuclear agreement are continuing. This plan faces a challenge in the Senate from Henry M. Jackson (D-Wash.) and others.

The White House provided no details of its own on the Carter-Gromyko talks yesterday, which were attended by advisers on both sides, including Vice President Mondale and presidential national security affairs adviser Zbigniew Brzezinski.

Gromyko described the discussion to reporters as an examination of "the fundamental question of the policy line of the United States toward the Soviet Union and the main policy line of the Soviet Union towards the United States."

National Security Council spokesman Jerrold Schecter said afterward that the White House talks "were to underscore the purpose of our relationship, not to reach decisions." He said the White House regarded Gromyko as "positive in his approach" and the talks were "constructive." CAPTION: Picture, President Carter and Soviet Foreign Minister Andrei A. Gromyko chatting in the White House yesterday. By [WORDS ILLEGIBLE] - The Washington Post