President Reagan and Soviet leader Mikhail Gorbachev began their long-awaited summit on an unexpectedly personal note today, departing from their schedule of formal sessions with aides present to hold nearly two hours of private talks in what spokesmen for both sides said was "a good atmosphere."

These private conversations, conducted under the terms of a U.S.-proposed news blackout on the substance and details of the talks, suddenly placed heavy reliance on the personalities and rapport of the two leaders as the center of this summit.

Soviet and U.S. officials interpreted the private talks between the two leaders, held with only their interpreters present, and the blackout as positive signs that Gorbachev and Reagan are interested in serious accomplishment at the summit.

"We must achieve a decision together," Gorbachev said in a tone of compromise as the two leaders posed for photographers at the beginning of the talks. "If someone will insist only on his own, I'm not sure it will be correct, that it will look like a decision. We are very much interdependent."

Reagan responded, "I agree with this."

After a total of four hours of talks, Gorbachev was asked this evening by reporters whether any agreement had been reached.

"We are working, we're continuing to work," he answered.

Late tonight, according to U.S. sources, the American team here was working on a prospective joint statement dealing with arms control that they would not otherwise describe. They emphasized, however, that a summit outcome which dealt in a meaningful way with arms control would depend on the two leaders reaching personal agreement Wednesday.

Earlier in the week, U.S. officials said one idea that was under consideration was a recommitment by both leaders to the arms control process and deep cuts in offensive nuclear weapons.

The personal touch of this summit also was reflected in an afternoon tea hosted by Nancy Reagan for Raisa Gorbachev at which the two first ladies invited each other to exchange visits to Washington and Moscow. This tea, scheduled to last 45 minutes, continued for one hour and 15 minutes. Gorbachev, the general secretary of the Soviet Communist Party, said after the morning session that the two leaders had talked about arms control and other issues in language that was "very calm, businesslike and pleasant." This description was echoed by American officials.

"The tone was good, the exchanges were good," said White House spokesman Larry Speakes after the afternoon meetings had concluded. "The opportunity for both to talk with each other concerning these major issues was carried on in atmosphere which the general secretary has described as businesslike, which we agree was an appropriate description."

Speakes said Reagan and Gorbachev spent an hour and 58 minutes together, with only their interpreters in two sessions in what was "clearly an unexpected development." They had planned to open the summit with only a 15-minute private meeting. The schedule then called for each of the two leaders to be joined by a team of six senior assistants and for the two delegations to conduct formal sessions. Instead, the opening morning session between Reagan and Gorbachev lasted for more than an hour.

And after formal talks had concluded in the afternoon, Reagan took Gorbachev by the arm and walked with him in the frigid Geneva weather for five minutes to a pool house near the lake, where they spent another 54 minutes in fireside conversation.

Gorbachev also spent 45 minutes during the day talking with former Democratic presidential candidate Jesse Jackson and a group of U.S. peace activists who brought him petitions with more than a million signatures calling for an end to nuclear testing and a nuclear weapons freeze.

Relating what Gorbachev had told him, Jackson said, "He said he and Ronald Reagan got down to serious business, and he made it clear his business was disarmament."

The day began with Speakes and his Soviet counterpart Leonid Zamyatin announcing at separate briefings that there would be a "blackout" on details of discussions at the summit sessions.

"Both sides have agreed this was appropriate in view of the serious and far-reaching topics that will be discussed on the agenda for both sides," Speakes said.

Each side did continue to brief reporters on the atmospherics of the talks and both Reagan and Gorbachev engaged in informal chats with reporters at photo opportunities. At dinner tonight, however, the blackout extended to the ceremonial toasts, which were not made public.

Soviet sources said that Speakes approached Zamyatin with the blackout proposal on Sunday, acting on the suggestion of U.S. Secretary of State George P. Shultz, who was said to believe that this would help make the talks productive. The Soviets, interpreting this step as evidence of U.S. seriousness of purpose, accepted the proposal the following day.

"There was a lot of propaganda going around," said Fyodor Burlatsky, a writer for the Moscow-based weekly Literary Gazette. "It was time to end that and get down to business."

Entering Fleur d'Eau, the 19th century chateau on the shore of Lake Geneva, where today's talks were hosted by Reagan, Gorbachev said in response to reporters' questions that he intended to raise with the president the possibility of bringing arms-control negotiators back to their ongoing talks in Geneva before Jan. 16, 1986, the date when the negotiations are scheduled to resume.

A senior U.S. official said yesterday that Reagan intended to raise this idea and that it was "most likely" to happen if Gorbachev agreed.

The presence of top Soviet negotiators Victor Karpov and Yuli Kvitsinsy, along with top U.S. arms control negotiators in Geneva, suggested that each side was holding open the chance for a last-minute arms-control agreement.

After today's meetings ended, White House chief of staff Donald T. Regan said that agreement to hold a follow-up session between the superpower leaders was "a possibility."

National Security Adviser Robert C. McFarlane said that the president, who called for more regular summits in a Nov. 9 radio speech, favored the idea in principle and might agree to it without actually setting a date for another summit.

Speakes said this morning, before these officials commented, that there has been "no agreement" on a decision to hold future summits and that he knew of no plans to call the arms-control negotiators back into session early.

Reagan said it was a "possibility" that the two leaders would stay on in Geneva through Thursday morning if there is an agreement to issue a statement on the discussions. Zamyatin echoed this possibility in another press briefing.

Because of the news blackout, however, it was not possible to ascertain whether the good mood displayed publicly by the leaders reflected a narrowing of the wide differences between them on arms control and other issues.

There was surmise in the American delegation that Reagan had used at least part of the time he spent alone with Gorbachev to expound on his proposal for missile defense, often called "Star Wars."

Entering a dinner tonight hosted by the Gorbachevs at the Soviet mission, the Soviet leader was asked whether he had changed his mind about space weapons.

"Keep that question," Gorbachev responded. "That is a question that should be explained at a press conference later."

Gorbachev gave no sense of flexibility in his opposition to Reagan's proposal, formally known as the Strategic Defense Initiative, in his speech to Jackson's group.

Soviet television broadcast seven minutes of the Gorbachev-Jackson meeting on its evening news report of the summit.

The portion appearing on the news show Vremya (Time) focused on Gorbachev's calls for ending the arms race.

The blackout was enforced on the toasts and other conversation between Reagan and Gorbachev at the dinner tonight by having a small pool of reporters quickly ushered in and out to see the scene.

The hold-down on news is scheduled to continue Wednesday, when the Soviets host the second day of talks.