The chief Kremlin spokesman today signaled Moscow's willingness to use the Geneva summit to begin a new phase in relations between the superpowers, projecting a positive assessment of the first meeting between U.S. and Soviet leaders in more than six years.

"It seems now the general secretary can engage in frank discussion" with the Americans, Leonid Zamyatin said. "That in itself is a big positive event. In such a limited space of time, the enormous amount of difficult problems that have accumulated cannot be resolved. It can only be a beginning."

Other Soviet officials quickly picked up the upbeat tone, but admitted that an easing of tension would leave them short of their goal of steering President Reagan away from his Strategic Defense Initiative plans.

"We didn't achieve our goal here," said one official, who asked not to be named. "The U.S. president believes very strongly in his SDI plans."

The subtle, but clearly forward-looking mood of Soviet officials today contrasted to the assessments they voiced before the summit that a firm Reagan stance on SDI threatened to deteriorate further the relationship and render the ongoing U.S.-Soviet arms talks here meaningless.

The Soviet diplomats and journalists circulating here seemed eager to consider the summit the beginning of a new Soviet-American dialogue. The summit, said Soviet commentator and journalist Fyodor Burlatsky, "is a new step in Soviet-American relations, a very important step because it can bring an end to the policy of confrontation."

Burlatsky, a Moscow professor and columnist for the Soviet weekly Literary Gazette said in an interview before the final word from Gorbachev and Reagan: "I have a feeling that the result is positive."

Other Soviet diplomats and journalists here said they shared the feeling. They cited the apparent close personal contact between the Soviet and American leaders as they engaged in their one-on-one meetings and some compromise agreements, including a planned trip by the Soviet leader to the United States next year, as evidence of the will on both sides for what one official called "a new beginning in the Soviet-American dialogue."

Soviet officials said they did not want to lose what they saw as an opportunity provided by the summit to end seven years of deteriorating relations.

"The fact that they met alone represents movement," said Oleg Bykov, deputy director of the Institute of World Economy and International Relations.

"The important thing is that a mutual political will emerge from this meeting. That alone would represent an advance towards addressing the arms control issues, and the wide gaps between the two sides on other issues."

The initial pessimism of Soviet officials was evident even after yesterday's Reagan-Gorbachev meetings when Col. Gen. Nikolai Chervov, the arms control expert on the Soviet general staff, repeated in an interview with a West German reporter here the view that a hard line by Reagan on SDI, or "Star Wars," in the meetings would worsen U.S.-Soviet relations.

Although the Soviets maintain a staunch opposition to SDI, they say they found Reagan "insistent," on continuing with research plans for the space defense system.

Gorbachev tried to explain to the president his arguments against SDI, Burlatsky said, "and maybe to push him to the understanding of our position."

Although he apparently did not succeed, Burlatsky added that "we don't want to let that stop discussion on other very important problems, including arms control."

Gorbachev, in various brief appearances during the course of the day, appeared to encourage the positive spirit through his smiles and quips to reporters.

Asked at a Swiss-hosted reception before tonight's dinner whether there would be any agreements, the Soviet leader said, "I hope there will be."

On the eve of a joint appearance by the two leaders, the Soviet officials spoke cautiously about the initial summit sessions.

But they indicated that Reagan gave Gorbachev a sense that he was interested in reducing U.S. strategic systems and speculated that the five hours of private conversations between the two leaders were spent reconciling their differences over SDI.

In interviews today, however, Soviet officials emphasized the general direction of the relationship instead of the differences over arms control.

Zamyatin's early afternoon press conference, in which he related Gorbachev's assessment of the sessions with Reagan as "frank" and "businesslike," swept in a mood of compromise among Soviet officials circulating here.

Gorbachev, in a speech in Moscow earlier this month, said that if the summit was conducted in a frank, businesslike way it would be successful.

Asked whether the two leaders had been able to strike any agreements, Zamyatin said, "I would very much like a compromise."

The officials interviewed after the press conference repeated Gorbachev's earlier calls for a return of the detente period of the early 1970s.

"We have had something that amounted to a second Cold War," one Soviet expert in U.S. affairs explained, "and now we think we're ready to have something like a second detente. It's a potential framework for a new beginning."

Soviet officials also confirmed that following his news conference Thursday, Gorbachev would report on the summit to East Bloc leaders in Prague.