Secretary of State George P. Shultz and Soviet Foreign Minister Andrei Gromyko discussed a U.S.-Soviet summit meeting during a six-hour conference here today but were unable to agree on a place for the proposed encounter between President Reagan and Soviet leader Mikhail Gorbachev.

Unusually guarded statements by U.S. and Soviet official gave no indication that an announcement of a Reagan-Gorbachev summit is near. The meeting is expected to take place in September or October.

Soviet spokesman Vladimir Lomeiko told reporters after the lengthy session that both sides had expressed "a certain interest" in a summit meeting.

U.S. officials would only repeat that Reagan has invited Gorbachev to meet, and that the president would like the meeting to take place in Washington. In the past, Soviet officials have indicated that Gorbachev plans to come to the United Nations in September, but they have not said whether he will be willing to make the trip from New York to Washington to see Reagan.

There have been suggestions that the two men might meet at the United Nations in September, at the opening of the General Assembly, or in October at a celebration of the world body's 40th anniversary. Administration officials have said the two men might meet "on the fringes" of the New York City site of the United Nations.

Shultz said after the meeting that his lengthy session with Gromyko, which took two hours longer than Shultz had planned, was devoted in "a heavy proportion" to arms control and particularly the Geneva negotiatons, now in recess until May 30.

Administration officials said all issues in today's talks were "thoroughly discussed" by Shultz and Gromyko but would not say whether there was any hint of forthcoming changes in position.

A Soviet statement read to reporters in English following today's meeting quoted Gromyko as complaining to Shultz about "unconstructive" U.S. positions at Geneva and calling for "strict adherence" to a tightly drawn relationship between cuts in offensive arms and limits on space weapons like those envisaged in the Reagan administration's Strategic Defense Initiative.

Gromyko, according to an account of the meeting by the Soviet news agency Tass, told Shultz that a halt to the design, testing and deployment of space weapons "could become the first important step" at the Geneva talks.

The U.S. attitude on this proposal "will serve as an indicator of the trend of its policy and intentions in the military field," Tass continued.

The Soviet insistence on limiting the "Star Wars" plan before discussing reductions in offensive weapons stymied progress in the first Geneva round, according to U.S. sources.

Shultz probed for the meaning of a statement by Gorbachev in Warsaw April 27 that was interpreted as announcing a Soviet offer to cut its strategic nuclear arms by 25 percent. But there was no report that Gromyko had confirmed such an offer, which was not put forward in the Geneva talks, according to U.S. officials.

Shultz, according to his aides, brought up the March 24 killing of U.S. liaison officer Maj. Arthur D. Nicholson by a Soviet sentry in East Germany and reaffirmed the U.S. demand for an apology and compensation for Nicholson's family, U.S. officials said.

There was no sign of a change in the Soviet stance, which is to express "regret" for the officer's death but to insist that it was the fault of the United States.

The occasion for today's Shultz-Gromyko meeting was the observance of the 30th anniversary of the signing of the Austrian State Treaty, which permitted this country to regain its sovereignty and independence after World War II.

U.S. officials held out the possibility that the two foreign ministers will meet again in early August in Helsinki at the 10th anniversary observance of the Helsinki European security accords. But the officials said Shultz's attendance would depend on a decision by the NATO alliance.

The meeting also covered several other aspects of U.S.-Soviet relations.

Lomeiko said Gromyko "emphasized" that "one of the main sources of tension" in the Middle East, Central America and elsewhere is the attempt of "certain circles" to impose their will on independent nations and their internal affairs.

U.S. briefers said the full array of Washington's regional concerns was discussed, but they provided no details.

Shultz said that he discussed human rights in the meeting, as he always does, but he did not say whether Gromyko took part in this discussion.

Lomeiko said Shultz was told that "the Soviet Union does not discuss questions that belong to the realm of internal affairs with anybody." U.S. spokesmen said human rights in the Soviet Unlon is a proper subject in part because of Soviet agreement to the human rights provisions of the Helsinki Accords.

Shultz said, "We discussed bilateral issues where some progress can be made," but he was not specific.

Lomeiko said the Soviet side intends to "build the structural basis" for the bilateral relationship.