Secretary of State George P. Shultz said yesterday that the succession in the Kremlin this week, coupled with other factors, has created a "moment of opportunity" for across-the-board improvement in U.S.-Soviet relations.

Shultz, fresh from reporting to President Reagan on his Moscow conversations with the new Soviet leader, Mikhail Gorbachev, said Reagan "firmly intends" to seize the moment for high-level dialogue and improvement in relations.

Both countries will have to do their part, Shultz emphasized, saying, "We and the Soviet Union carry an enormous responsibility for preserving peace and fostering better understanding."

With two "businesslike people" now in charge in Washington and Moscow, and arms talks under way again in Geneva, Shultz told a news conference, "I think there is an important responsibility on both sides to make every effort to take advantage of this moment of opportunity."

Shultz gave public approval to a summit meeting between Reagan and Gorbachev without the usual qualifications that such a session must be "well-prepared" and promise constructive results.

"The president would be glad to see Mr. Gorbachev here in the United States, at his convenience . . . . I think it would be a constructive thing for them to meet," Shultz said.

The secretary declined to characterize Gorbachev's response to Reagan's invitation, which was presented by Vice President Bush and Shultz in a 90-minute conversation Wednesday after the funeral of Soviet President Konstantin Chernenko.

State Department officials said Gorbachev is being invited to come to the United States because it is "their turn" to visit. Officials said the last two summit meetings on the soil of either superpower were President Richard M. Nixon's 1974 visit to Moscow and President Gerald R. Ford's 1974 meeting with Soviet leader Leonid Brezhnev in Vladivostok in Soviet Asia.

In a statement that Reagan approved shortly before the news conference, Shultz listed four areas for potential improvement with the Soviets:

* Early agreement in the new nuclear and space arms talks that opened Tuesday in Geneva. The main U.S. objective, Shultz said, is "deep reductions in offensive nuclear arms" with a secondary goal of "a longer-term dialogue" about strategic defense, including Reagan's "Star Wars" plan.

"We see no obstacles from either side to getting down to specifics in these talks," Shultz said.

Officials said the three teams of negotiators in Geneva on space and defensive arms, long-range offensive arms and intermediate-range offensive arms, will meet again as a group Tuesday and Thursday at Soviet request before breaking into three working sessions the following week. The Soviets, by insisting on joint meetings of all three groups, emphasize the interrelationship of Star Wars, which they strongly oppose, to cuts in offensive arms.

* Better understanding on solutions "in regions of crisis and potential confrontation."

Reagan has proposed periodic consultations at "policy level" to discuss areas of regional conflict. In the first such recent discussion, Richard W. Murphy assistant secretary of state for Near East and South Asian affairs, and his Soviet Foreign Ministry counterpart, Vladimir Polyakov, met Feb. 19-20 in Vienna on the Middle East.

* Progress on human rights issues. The United States is looking to a combination of "dialogue and confidential diplomacy" as well as better Soviet understanding of the broad repercussions of improvements.

Assistant Secretary of State Elliott Abrams said in an interview that "it is conceivable" that a Soviet shift on human rights issues is in the offing, though there is no evidence that such a shift has taken place. Among the signs of possible progress, he said, is an invitation to Edgar Bronfman, president of the World Jewish Congress, to visit Moscow for discussion of human rights issues.

* Expansion of cooperation between the two nations, including "people-to-people contacts, cultural exchanges, airline safety, nonstrategic trade and other areas of mutual interest."

Shultz said discussions are taking place with the Soviets in several of these fields.

While speaking of Soviet-American relations in a mostly positive and hopeful fashion, Shultz also expressed caution against high expectations.

"Objective differences of values and national interest" in all four areas will be "difficult to resolve," Shultz said. He also called for "a healthy measure of realism" along with optimism, referring to "a history which has not always fulfilled our expectations."

Gorbachev "gives the feeling of a very capable, energetic person, who is businesslike . . . . He seems to be well-informed and well-prepared and gets right at the issues in a conversational kind of form," Shultz said.

"Whether it turns out that you can do business," as suggested by British Prime Minister Margaret Thatcher's remarks, "is another matter," Shultz said, suggesting a reservation on this point.

Asked about the potential impact on the United States of improvements in Sino-Soviet relations, Shultz repeated the Chinese conditions for major improvements in their ties with Moscow. This seemed to suggest a U.S. expectation that Peking will stick to these requirements, which include Soviet troop cuts along the Sino-Soviet border and Soviet policy changes in Cambodia and Afghanistan, despite the warming atmosphere of exchanges this week between the two giants of international communism.