Just before the two superpower leaders read their summit statements in Geneva Thursday, President Reagan turned to Soviet leader Mikhail Gorbachev and said, "I bet the hard-liners in both our countries are bleeding when we shake hands." Gorbachev nodded in agreement.

This story was recounted by Reagan to senior advisers yesterday to illustrate his view that the Geneva summit was the promising start of a process of improved U.S.-Soviet dialogue and possible arms-control agreement that administration officials expect to intensify in the months and years ahead.

Reagan told his Cabinet that when he and Gorbachev parted, "we didn't just say goodbye." Instead, he said the Soviet leader reiterated that they should stay in touch before their next summit meeting. "I have to believe that . . . they share with us the desire to get something done, and to get things straightened out," Reagan said.

For the president, the summit was a telling personal experience. He emerged from it, one White House official said, believing that "what Gorbachev was doing was reflective not only of his ideology but of his genuine belief." After a political career in which Reagan has emphasized the untrustworthiness of the Soviets, the president yesterday expressed his respect for Gorbachev and expressed optimism about future U.S.-Soviet negotiations.

Reagan told reporters in the White House family theater yesterday that it had been "very worthwhile" to "erase these . . . suspicions" of each other in his five hours of private meetings with Gorbachev.

"And I think I'm some judge of acting so I don't think he was acting," the president said. "He, I believe, is just as sincere as we are in wanting an answer."

Senior officials who reviewed the summit yesterday said that the Geneva meeting, while producing few tangible results on arms control and other thorny issues which divide the superpowers, accomplished Reagan's goal of achieving a "fresh start" in U.S.-Soviet relations.

They placed particular emphasis on the momentum for agreement they said had been provided by the decisions to have future summits, with Gorbachev visiting the United States next year and Reagan going to the Soviet Union in 1987.

A senior White House official said that additional summits will place pressure on both leaders and their arms-control negotiators to come up with an agreement to curb nuclear arms. This time, he said, the meeting was a "success" because it came after six years without summits and open hostility in U.S.-Soviet relations. "But by the time you get to the third meeting, is it a success if you just agree to meet for the fourth time?" this official said. "You do have a clock running as to whether there is going to be a closing of positions . Both sides have started to build pressure for movement. It wasn't there before."

The agreement to seek additional summits was endorsed by Reagan in a radio speech on Nov. 9 and pursued by him at Geneva. About this time Reagan, who had opposed all prior suggestions to go to Moscow, surprised his advisers by telling them that he would agree to future summits even if Gorbachev insisted the next one be held in the Soviet Union.

As it turned out, however, Gorbachev readily agreed to Reagan's suggestion that the next summit should be held in the United States.

The moment of decision came in the parking lot on the first day of the summit while Reagan and Gorbachev were strolling back to a Swiss chateau after a 48-minute fireside talk in a pool house on the shores of Lake Geneva.

Reagan said that Gorbachev said "something that I took as a kind of cue line," and the president quickly invited him to come to the United States in 1986.

Gorbachev immediately accepted and responded, "And I invite you to come to a subsequent meeting in Moscow," which Reagan in turn accepted.

"And I think that when we both went in and told our teams that this was all settled, they almost fell down," Reagan said. "There was no fight there."

The two leaders did "fight" -- or at least disagree in the strongest terms -- over Reagan's missile defense plan, the Strategic Defense Initiative (SDI), and over human rights, where Gorbachev responded by criticizing human rights practices in the United States.

Conservatives in the administration were generally delighted that the president had refused to give ground on SDI, and one official said that Reagan had dispelled the "myth" that he has "to give up 'Star Wars' to get along with the Soviets."

But the dominant view among the president's advisers yesterday was that he had started down a course at Geneva which will not be easily reversed. By agreeing to the series of summits with Gorbachev and pledging to push for agreements in the interim, these advisers said, Reagan had staked the course of his second-term presidency on bargaining with the Soviets instead of confronting them.

In the process he has also diminished talk of a "lame-duck" presidency in which Reagan would become little more than a caretaker after the 1986 midterm elections.