Layers of ice broke when President Reagan told a Russian proverb in his welcoming remarks yesterday, bringing a smile across Soviet leader Mikhail Gorbachev's face and throughout the crowd of Soviets scattered across the White House lawn.

But Reagan's call for the "beginning of a working relationship that will enable us to tackle other issues," just before he and Gorbachev signed the treaty to eliminate medium- and shorter-range missiles, touched off the strongest positive reactions among Soviet officials and journalists here.

Soviet officials said they were moved by both the style and the substance of Reagan's appeal, by his use of Russian anecdotes and words and his proposal for closer U.S.-Soviet ties.

Despite the U.S. efforts to complete the missile treaty signed by Reagan and Gorbachev yesterday, Moscow cast doubts on Reagan's motives and commitment to continued improvement in the countries' relations during the days before the summit.

But the opening day's events calmed Soviet fears that Reagan would end efforts at a rapprochement with Moscow after the treaty signing, and excited new expectations among some Soviets that a pact under negotiation to cut strategic arsenals and other agreements could be resolved.

Although the future arms talks also depend on Reagan's negotiating position, Soviet officials credited Reagan yesterday with setting a tone for closer ties with Gorbachev during Reagan's last 13 months in office. "For a first step in a new relationship," one Soviet official said in an interview, "it was just right."

"I have heard some new words in the president's welcoming remarks," Gorbachev said in his brief morning speech, "and I welcome his comments."

Other Soviet officials noted a more profound change in Reagan. After watching his speech on the White House lawn, Oleg Bykov said the president seemed "subdued."

"I was most impressed by the positive expectations he awakened for relations in the future," said Bykov, deputy director of the World Economy Institute. "It was not superficial or an act. It had the ring of sincerity . . . . There were, of course, a few words for those who do not agree, too. But on the whole, the thrust was unusually accommodating."

Reagan's speeches yesterday also gave Nikolai Yefimov, deputy editor of the Soviet government newspaper Izvestia, the impression that the president "had changed."

"There was a change in both leaders," Yefimov said. "It might be because he was playing host. But there was some important change there, a commitment to better relations in the future."

"In a way it is unfortunate that Reagan is leaving {office} soon," said an editor for the Soviet Communist Party newspaper Pravda, who asked not to be named. "He has become a known quantity to us. When he jokes, we know it's a joke. He can get away with saying things that someone else would not get away with."

It was, in part, Reagan's use of jokes and Russian proverbs that set the tone for the positive development in the day's events.

"To quote a Russian proverb," he said, smiling, before signing the missile treaty, "as you can see, I'm becoming quite an expert in Russian proverbs: the harvest comes more from the sweat than from the dew."

Reagan then lightheartedly proposed that the negotiators "get some well-deserved rest," but Gorbachev promptly shot back, "We're not going to do that."

The spirited public banter between Reagan and Gorbachev over the course of the day reinforced the mood of cooperation between the two. Asked about the chemistry between the two leaders in the opening day's talks, Foreign Ministry spokesman Gennadi Gerasimov said, "I think it's a little early for chemical analysis."

Bykov cautioned that a lighthearted tone can sometimes backfire in encounters between adversaries such as Gorbachev and Reagan. But this time, he added, Reagan was "modest in his approach."

Despite the mood of good will Reagan and Gorbachev established, Soviet officials cautioned that obstacles on space weapons remain. Gorbachev signaled yesterday that the issue will surface during his visit, saying that he favored strategic cuts in the context of "a firm guarantee of strategic stability."

"Strategic stability" is interpreted by arms control experts as a Soviet buzzword for controls on Reagan's Strategic Defense Initiative, viewed by Moscow as a threat to stable arms control.