Six hours of talks between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei Gromyko produced no early agreement on a summit meeting between leaders of the two countries and no meeting of the minds on any key issue in the Geneva arms negotiations, according to U.S. and diplomatic sources.

Shultz, interviewed on Austrian state television before leaving for Washington, said today that "there's nothing to add to what's already known" about the possibility of a meeting between President Reagan and Soviet leader Mikhail Gorbachev.

Shultz said that while both sides have approved the principle of the meeting in a previous exchange of letters, "as yet we've not been able to settle on when or where that meeting will take place."

Other officials familiar with the course of the talks said that the subject of a possible Reagan-Gorbachev meeting this fall never came up.

In Washington, administration sources said U.S. officials were under instructions not to raise the summit issue, but to respond positively if the Soviets accepted Reagan's invitation for a meeting in the United States. This posture apparently was based on an assessment that Moscow was not yet ready to deal definitively with the summit question and the feeling among U.S. officials that the next move is up to the Kremlin since the specific invitation had been an American initiative.

Despite hopes raised by a new leader in Moscow and new arms control negotiations in Geneva, the United States and the Soviet Union, in the opinion of concerned allied diplomats, may be settling into an impasse in their relations, generating a high level of international tension.

This morning Shultz and U.S. arms adviser Paul H. Nitze briefed British, French, West German and Italian delegations on the Shultz-Gromyko session of the day before.

West German Foreign Minister Hans-Dietrich Genscher, according to West German sources, called for a far-reaching reconsideration of North Atlantic Treaty Organization strategy toward the Soviet Union in the Gorbachev era. Such a high-level discussion would be possible at the NATO foreign ministers' conference in Lisbon June 5.

Shultz told reporters, however, that he doesn't sense pressure to "throw in the towel" on alliance strategy just three months into the Gorbachev era. He said the existing strategy had been fashioned for "the long haul."

The Geneva arms negotiations, now in recess after an unproductive first six weeks, are to resume May 30. The Shultz-Gromyko meeting Tuesday, which centered on the arms talks more than any other issue, left only a slender hope for early changes in the Soviet position.

U.S. sources said Gromyko, under prodding from Shultz, seemed to back away to some degree from a Soviet negotiating position in Geneva that, in effect, made the banning of work on Reagan's Strategic Defense Initiative (SDI) a "precondition" to negotiation of any cuts in offensive arms.

The communique from the Shultz-Gromyko meeting Jan. 7-8 that established the basis for the new Geneva arms talks said the "complex of issues" concerning both offensive arms and space arms would be "considered and resolved in their interrelationship."

At the negotiations that began March 12, according to U.S. accounts, the Soviets refused even to consider U.S. proposals for cuts in offensive arms, saying that progress would be impossible until the United States agrees to ban "space-strike arms," including research into SDI.

Tuesday, according to a U.S. participant, Gromyko repeated the Soviet insistence at Geneva that "scientific research" into SDI be banned along with testing, development and deployment. Gromyko's justification, according to this account, was that the aim of the "scientific research" is to provide the basis for weapons prohibited by the 1972 antiballistic missile treaty.

On the other hand, Gromyko reportedly did not assert Tuesday that a prior U.S.-Soviet agreement to ban space weapons is necessary before considering cuts in offensive arms.

"In my mind," Shultz told reporters, "we confirmed what I understood about the structure and linkages of the negotiations." He added, "I hope things will progress along this line."

Gromyko reportedly said nothing to Shultz Tuesday about a one-fourth cut in strategic offensive launchers, which had been proposed by the Soviets in the 1982-83 Strategic Arms Reduction Talks (START) and was mentioned by Gorbachev in a speech April 27.