President Reagan and Soviet leader Mikhail Gorbachev today wound up their person-to-person diplomacy with the announcement that Gorbachev has accepted an invitation to visit the United States and that Reagan has agreed to visit the Soviet Union.

In statements released at the end of the first U.S.-Soviet summit in six years, Reagan and Gorbachev agreed to "accelerate the work" in the nuclear and space-arms negotiation, but they gave no indication that a breakthrough had been reached in this crucial area.

A joint statement called for "early progress" where there is common ground, especially in reduction of offensive nuclear arms, but no mention at all was made of the touchstone issue of strategic defense.

Reagan and Gorbachev announced several agreements including implementation of the already signed Northern Pacific Air Safety accord that is aimed at preventing a repeat of the Soviet downing of a Korean airliner in September 1983 and an agreement on the opening of consulates in Kiev and New York.

The two leaders did not specify dates for their next summit, but agreed "to meet again in the nearest future." U.S. officials said they expected Gorbachev to visit the United States next year and Reagan to visit the Soviet Union in 1987.

In their final statement read to reporters at Geneva's International Conference Center, the two leaders, summing up their intense personal discussions here, said: "While acknowledging the differences in their systems and approaches to international issues some greater understanding of each side's view was achieved by the two leaders. They agreed about the need to improve U.S.-Soviet relations in the international situation as a whole."

The joint statement provided the first details of the substance of the nine hours of talks -- more than half of them in private between the two leaders accompanied only by interpreters.

But both sides portrayed the summit as having given new impetus to U.S.-Soviet relations.

"The news is so good we're going to hold it 'til tomorrow," Reagan quipped to a reporter at a cordial farewell dinner for Gorbachev last night. White House spokesman Larry Speakes said there had been "good progress" in yesterday's talks.

Soviet spokesman Leonid Zamyatin echoed this generally upbeat tone, saying the meeting "itself is a big, positive event."

U.S. sources had said earlier that the two sides would agree to nonspecific reaffirmation of the goal of nuclear arms reductions.

It was also likely that a new program of nuclear-fusion research for peaceful purposes that involves the United States, the Soviet Union and other advanced industrial nations would be announced, these sources had said.

However, there was no sign that the two sides had made major progress on the crucial issue of arms control. There appeared to be no closing of the wide gap between the United States and the Soviet Union on differences over Reagan's missile defense project.

Speakes appeared just before midnight in a crowded hotel ballroom that has been used for White House briefings during the summit to announce that the two leaders would appear in what he called "a ceremony." He would not elaborate on its contents or say whether any breakthroughs had been achieved on arms control.

Senior advisers on both sides had been holding intensive meetings on arms control and other issues from Tuesday through last night, officials said.

Speakes said that Reagan and Gorbachev had received a report on disputed issues from their advisers during dinner, which they concluded by shaking hands on the agreements they will announce today.

Gorbachev postponed a scheduled news conference here from 10 a.m. to 11 a.m. (5 a.m. Washington time) so that the two leaders could make the joint appearance.

Reagan, who Speakes said will not hold a news conference, will leave early in the afternoon for Brussels, where he will report on the results of the talks to NATO allies. The 74-year-old president, on what will be a 20-hour workday for him, will then fly to Washington and deliver a nationally televised speech to a joint session of Congress tonight.

In an unusually extensive effort to brief friends and foes, assistant secretaries of state will travel to Western Europe, Latin America, Africa and the Middle East to report results of the summit to world leaders, and special arms adviser Edward Rowny will travel to Eastern Europe and Czechoslovakia, U.S. officials said today.

Soviet sources said that Gorbachev will fly from here to Prague to brief his Warsaw Pact allies.

The Geneva summit was the first time that either Reagan or Gorbachev had met the leader of the rival superpower and the first U.S.-Soviet summit since 1979.

Reagan, considered the most outspokenly anti-Soviet president in U.S. history, appeared to have achieved a personal rapport with the new Soviet leader, who at 54 is 20 years younger than the president.

While only a 15-minute personal meeting had been scheduled in advance, the two men spent nearly five hours together with only interpreters present, a more intense period of discussion than Reagan has held with any other foreign leader. In contrast, they spent only four hours talking to each other with their advisers present, in the usual format for such presidential meetings.

Specific agreements that will be announced today, most of which had been expected, were said to include an agreement to renew the U.S.-Soviet dialogue in a host of channels, including regular summit meetings involving reciprocal visits to one another's capitals and intensified meetings of lower-level officials.

Under protocol rules, the next summit would be expected to take place in the United States. The last two summits held in the territory of either superpower took place in the Soviet Union.

Cultural exchange agreements totaling 41 pages have been prepared for signature. These would restart officially sponsored exchanges of theatrical and artistic groups and major exhibits that were suspended after the Soviet invasion of Afghanistan on Dec. 24, 1979.

Hours after Reagan and Gorbachev had concluded their final business meeting and dinner last night, their negotiators continued to work on statements to be issued on arms control, U.S. sources said.

The possibility of progress on arms control arose in part from new Soviet proposals that Gorbachev brought to Geneva, according to sources on both sides.

Confirmation that arms issues were under active consideration came from White House spokesman Larry Speakes, who said that senior arms control adviser Paul H. Nitze and Assistant Defense Secretary Richard Perle, the Pentagon arms control specialist, had joined a meeting of U.S. and Soviet senior advisers at the Soviet mission yesterday afternoon.

Speakes set aside the "blackout" rule that was imposed on the talks at U.S. initiative Tuesday to tell reporters that "there are broad areas of agreement and other areas where discussions must take place."

Some administration conservatives privately lamented what they considered insufficient focus on human rights issues at the summit. When Speakes reviewed the subject area of discussion yesterday, he at first omitted human rights. But Reagan had stressed in interviews before the summit that he would deal with this issue privately with Gorbachev, on the grounds that he had decided the best way to deal with it was through quiet diplomacy.

Reagan and Gorbachev spent an hour and nine minutes in private discussions yesterday morning solely with interpreters and another hour and 44 minutes in two sessions yesterday afternoon. Speakes said this demonstrated that the personal chemistry between the two men was "very good" and that they are "two leaders who can communicate with each other."

Speakes, under heavy questioning, said that an "adequate historical, political and diplomatic record" was being kept of the private conversations.

The Soviets hosted the second day of the talks. Entering the Soviet mission this morning, Gorbachev was asked in Russian if the differences had been narrowed on security issues.

"The meeting is not over yet," he replied, then confirmed that he would hold a news conference today after the summit concludes.

When Reagan and Gorbachev were not meeting with each other or exchanging views at a plenary session -- where they were surrounded by their senior advisers -- they spent their time fending off questions at photo-taking sessions.

Gorbachev told reporters that "we had a very lively discussion of everything" and also described the talks as "frank, businesslike" and "responsible."

When a reporter asked in English if there was any "table pounding," Gorbachev replied: "I think this is not going to happen. This is not going to happen today, or tomorrow or in the future."

The Soviet leader also disclosed that he and Reagan had "begun discussing" whether he should visit the United States for a future summit. When Reagan was asked whether he would like to see Gorbachev visit the United States, he replied, "Of course."

Outwardly, the friendly mood and "good atmosphere" that spokesmen for both sides had taken note of Tuesday continued on the second day of the summit.

When the talks opened yesterday, Gorbachev welcomed the president at the end of a red carpet, then led him up three flights of stairs into the mission. On the way in, the two men chatted and Gorbachev made animated gestures that were repeated in exaggerated form by Reagan's interpreter.

Speakes said the two leaders had exchanged gifts. Reagan gave Gorbachev a Colonial Williamsburg Chippendale-style box made of mahogany with a silver top and a desk set of two pens with the theme "peace through communications," selected in honor of the l0th anniversary of the U.S.-Soviet Apollo-Soyuz space mission. Gorbachev gave Reagan a set of bronze medallions in a leather case, representing the 15 republics of the Soviet Union. In the center was a medallion with a Soviet flag on one side and the hammer-and-sickle emblem of communism on the other.