Soviet leader Mikhail S. Gorbachev told President Reagan Tuesday it may be "time to bang our fists on the table" to prod negotiators working on a treaty halving strategic nuclear arms stockpiles. But it was clear that an agreement would not come at this week's summit.

"I'll do anything that works," Reagan said.Officials in both delegations said the goal was to reach an agreement before Reagan leaves office next January. Gennady Gerasimov, the Soviet Foreign Ministry spokesman, said that "unfortunately, there will be no more signings" beyond minor agreements finalized Tuesday.

On their third day of talks, Reagan and Gorbachev met in the Soviet leader's Kremlin office, sitting beneath a portrait of Karl Marx. After their discussions, they took an unscheduled stroll on Red Square past the tomb of Lenin and shook hands with surprised tourists. "Wonderful," Reagan said of the square.

Reagan appeared tired and had difficulty following questions from reporters. White House spokesman Marlin Fitzwater said Reagan had slept poorly and that everyone in the delegation was tired, despite a four-day rest stop in Helsinki.

Nancy Reagan, asked about her husband, said, "He sleeps fine." Fitzwater said Reagan was in good health and "his stamina is just fine."

At a meeting with Soviet students, Reagan was asked about his impressions of Soviet dissidents and refuseniks with whom he met. Soviet newspapers described one of the dissidents as a collaborator with the Fascists during World War II. The president said he knew nothing about this allegation.

Reagan said Gorbachev "has been most helpful and agreeable about correcting" the problems incurred by those groups. "We have the same type of thing happen in our country," Reagan said, blaming it on bureaucrats.

The Soviet leader expressed new hopes for completing a major arms treaty, but it was not clear whether he was talking about getting it done by summit's end - or merely before Reagan`s term concludes next January. Soviet and American officials have said repeatedly they do not expect a strategic arms pact (START) to be concluded here.

During an encounter with reporters, Reagan was asked if he still believed the Soviet Union was an "evil empire," as he has called it in the past.

Standing next to his host, Reagan said he no longer thought that way. "I was talking about another time, another era," the president said.

The leaders also watched and joined in the applause as Secretary of State George P. Shultz and Soviet Foreign Minister Eduard A. Shevardnadze signed several secondary agreements, including a pair of arms accords. Under one such pact agreed to in Moscow, the superpowers will notify each other of the time, place and intended target of intercontinental-range missiles tests.

Reagan, continuing his public relations offensive to promote freedom and human rights in the Soviet Union, met over lunch at the House of Writers with artists, filmmakers and writers.

Talking to some of the Soviet Union's leading intellectuals, he discussed how an actor could become president - explaining that both artists and political leaders had to be able to grasp a vision and to put it into life.

"By the way, I`ve found that Mr. Gorbachev has the ability to grasp and hold a vision, and I respect him for that," Reagan said.

Later, in an address prepared for delivery to students at Moscow State University, Reagan said the young people were living "in one of the most exciting, hopeful times in Soviet history" when "the first breath of freedom stirs the air."

He said "we are hopeful that the promise of reform will be fulfilled."

At the Kremlin meeting, Reagan appeared to dig in his heels on his Strategic Defense Initiative missile defense plan, one of the key obstacles to agreement on a strategic arms treaty. "It's never been a part of the negotiations," he said in response to a question.

Without addressing "Star Wars," Gorbachev said he was confident there would be progress on arms issues.

"And I'm sure that if the president makes good use of his time that we have remaining, I'm sure that we will be able to prepare the treaty," Gorbachev said.

At that point, a reporter asked Reagan if he, too, thought a treaty could be concluded. "Yes, I'm very pleased to hear what they're saying." Asked again if a treaty was possible, Gorbachev stepped in to answer, saying, "If that question is to me, yes I think a START treaty is possible."

The Soviet leader recalled that he and Reagan, at their first summit in Geneva in 1985, had reached an impasse at one point. He said that at that point, "the president said, `Well, let's stamp our fists on the table.' `I said all right,' and by morning everything was agreed, the Geneva negotiations were successfully completed."

"Maybe now it is again a time to bang our fists on the table once again," Gorbachev said.

Asked by a reporter if he agreed, Reagan said, "I'll do anything that works."