Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko met here for nearly seven hours today in an effort to arrange a new series of arms control negotiations covering offensive nuclear weapons and weapons in space. There was no report from either side about the results.

U.S. officials, who were unusually secretive about the day's events, indicated that mixed signals from the Soviet side gave them no reliable way of predicting what the final outcome will be.

An announcment of the results is expected at the end of Tuesday's meetings.

Shultz had a big smile -- but not a single word of reply -- to questions from reporters as he returned to his hotel after meeting Gromyko for 3 1/2 hours this morning and 3 hours and 20 minutes this afternoon. Following the official meetings, Shultz was host at a reception at the U.S. mission for Gromyko and his party.

A U.S. official familiar with the proceedings said most of the morning meeting was taken up by Shultz and Gromyko reading prepared positions to one another. That meeting went on an hour longer than was planned, throwing the rest of the day off schedule.

Reporters observed that Shultz, Gromyko and others on the two sides seemed more cordial toward each other as the day went on, especially at the U.S. cocktail reception for the Soviets, which featured vodka as well as Scotch, bourbon and other spirits.

Journalists were cautioned not to place any special significance on the fact that the U.S. delegation sponsored a social gathering for its Soviet counterpart despite the many months of heightened antipathy and tension between the two governments.

A Soviet source said Shultz had proposed a cocktail reception to Gromyko weeks before today's meetings with the explanation that he sought an opportunity for his large and diverse team of administration officials to have at least a minimal contact with the visitors from Moscow. The source said Gromyko initially was negative about Shultz' request but finally agreed.

Taking part in the actual discussions today in addition to Shultz and Gromyko were only three officials on each side, plus a note-taker and an interpreter for each delegation.

Shultz' team was National Security Adviser Robert C. McFarlane, special arms adviser Paul H. Nitze and Arthur Hartman, the U.S. ambassador to the Soviet Union.

The Soviet team was Gromyko, Deputy Foreign Minister Georgi M. Kornienko, arms negotiator Viktor P. Karpov and Anatoliy F. Dobrynin, the ambassador to the United States.

Other members of the high-powered U.S. delegation, including strategic arms negotiator Gen. Edward Rowny, Assistant Secretary of State Richard Burt and Assistant Secretary of Defense Richard Perle, caucused at the U.S. mission to hear reports on the intimate bargaining sessions led by the two foreign ministers.

The announced purpose of the meetings today and Tuesday is to establish the "subject and objectives" of full-scale negotiations between the two nuclear superpowers on "the whole range of questions concerning nuclear and outer space arms."

U.S.-Soviet strategic and medium-range arms control negotiations have been suspended for more than a year after a Soviet walkout. Weaponry in outer space, which has not been the subject of U.S.-Soviet negotiation during the Reagan administration, has taken on central importance for Moscow since the early 1983 Reagan announcement of a Strategic Defense Initiative, popularly known as the "Star Wars" plan, to intercept and destroy enemy missiles in outer space.

So tight-lipped were U.S. officials today that the new State Department spokesman, former NBC newsman Bernard Kalb, was not seen at all except to tell a group of reporters who confronted him, "There will be no briefings while the discussions are underway."

Even the barebones announcement that the morning session of the talks lasted an hour longer than had been planned was published by the U.S. mission under the written heading, "On Background," meaning that the source of the information should not be named.

When a television journalist engaged a member of the U.S. delegation in conversation, another U.S. official moved in quickly to take the delegation member away.

In the hotel where officials and reporters are staying, a member of the U.S. delegation declined even to sit down with journalists having a late night supper in the coffee shop, saying that to do so might cause him "to lose my job."

Just about the only direct quotation from a U.S. negotiator was attributed to McFarlane by Olga Maitland, who heads a prodefense organization in London and writes a gossip column for a mass circulation London newspaper.

After a previously arranged photo session with McFarlane following today's talks, Maitland issued a press released quoting McFarlane as telling her, "Regarding SDI Strategic Defense Initiative , it is a defensive system. It is not that the Russians do not understand. They understand everything. They have done considerable research themselves and do not want to give up their advantage."

"At this stage," McFarlane was quoted as adding, "it is not the time to be feeling either optimistic or not" about the negotiations.

A spokesman for McFarlane later denied that he had said this to his visitor. But Maitland said she wrote the press release immediately after her 10-minute conversation and photo session with McFarlane, and that the quotations had been approved at the time by three U.S. officials.

The Soviet side was no more forthcoming, answering no questions from reporters. Asked by a reporter to give some indication of the progress of the talks, Gromyko at the reception tonight replied, "No interviews." He then held up his palm in a gesture to stop further inquiry, saying without explanation, "No fair."

As was the case today, the talks Tuesday are to begin at the Soviet mission here in the morning. If a further session is required, the talks are to be completed in an afternoon session at the U.S. mission.