The new leadership of the Soviet Union has been given a precise picture of action the Reagan administration considers necessary for improving relations with the United States and now will "have to decide their own answer as to what kind of a road they choose," Secretary of State George P. Shultz said yesterday.

Shultz, speaking within hours of Moscow's announcement that Yuri V. Andropov would succeed Leonid I. Brezhnev as general secretary of the communist party, said the Reagan administration took great care to lay down a precise marker for the Soviet Union earlier this fall at a time when it clearly was nearing a period of transition.

That marker, as outlined publicly for the first time by Shultz yesterday at a breakfast with Washington Post editors and reporters, would require major steps by the new Soviet leaders in a number of areas where they likely will find it difficult to move.

While much of the discussion yesterday centered on the U.S. assessment of the change of leadership in the Kremlin, Shultz also said:

* The United States has seen "tremendous movement" on the part of the Arabs since President Reagan's Sept. 1 peace initiative, "really gigantic." He added that "clearly there is an additional step that is highly desirable and that is a statement by King Hussein with the proper Arab support and Palestinian involvement that he is ready to talk explicitly with Mr. Begin."

Israeli Prime Minister Menachem Begin is to meet with President Reagan next Friday. Like other administration spokesmen, Shultz said Israeli settlement activity was "provocative" and not "constructive in any way."

* He is planning a trip to China early next year. State Department officials have indicated that Shultz wanted to go to China, but the timing had remained uncertain. The trip became all the more important following recent Chinese-Soviet talks during which the two communist powers agreed to continue negotiations on their long-range relations.

Shultz indicated that Moscow would not necessarily have to move in all the areas on the U.S. list for relations to improve, but he outlined the following areas for action by the Kremlin: Soviet withdrawal from Afghanistan, a relaxation in Poland, a Vietnamese withdrawal from Cambodia, and progress toward arms reductions in any of the three negotiations now under way.

He then cited two categories in the area of human rights: "We could see Mr. Anatoly Scharansky given a chance to live, and we could see a greater willingness on the part of the Soviet Union to let people who want to leave their country leave." (Scharansky, a Soviet dissident, has been imprisoned and is reported quite ill.)

Shultz, as President Reagan did in formal messages and in his news conference Thursday night, stressed the desire for improved relations with the Soviet Union, saying that ties currently are "strained" and that "there is much room for improvement."

While his list for possible action by Moscow was a long one, the secretary of state returned time and again to two steps the United States might take in response: mutual arms reduction and possible increased trade. He carefully couched the latter in the context of the current negotiations with North Atlantic Treaty Organization allies for an East-West agreement on economic relations with the Soviet Union.

Shultz said that he had outlined the U.S. agenda for improved relations in more than seven hours of talks with Soviet Foreign Minister Andrei Gromyko at the United Nations the last week of September and the first week of October. He reiterated the U.S. position yesterday, noting that the new leaders in the Kremlin are new in name only; they all have been part of the leadership group under Brezhnev and are of his generation.

Yet, he said, "I suppose it is always possible when you have new leaders in any country...a new person has an opportunity to look over the situation and see what if any directions that may differ with the past are desirable.

"In that sense, making it clear to the new Soviet leadership what the policy of the United States is and what can be expected from the United States is very important to do. And to a very considerable extent, in the lengthy discussions I had with Foreign Minister Gromyko, that was our object, to in a sense create a transcript that presumably will be read and to let that be a statement of what our policies are and what they will be and what response can be expected from us under what circumstances."

When asked if the reported Soviet proposal at the Geneva arms talks for both sides to reduce their missile and bomber forces to 1,800 was a concrete offer, Shultz said, "we don't consider that any truly significant offer has been placed on the table."

Previously, White House officials had said privately that the Soviet proposal at the strategic arms talks, while falling far short of the administration ideas on reductions, was an encouraging sign.

Shultz linked the arms reduction issue to the budget pressures facing both governments.

An agreed reduction of nuclear or conventional arms "would take some of the burden off their economy," he said. "We are conscious of the burden of defense spending in this country, but it is nothing in comparison to the relative burden that they are placing on their people."

Similarly, he cited the mutual benefits of trade, noting that some trade takes place now, "but it is on a very modest and I would say hesitant scale."

Shultz said that in his conversation with Gromyko, he underscored most heavily the need for Soviet action involving the human dimension.

"Human beings are very important to us," he said. "It puzzles me why a country wants people in its country who don't want to be there. So letting people leave who want to leave would be a very welcome sign. I don't mean by bringing this out in any way lessens the importance of arms control. . . . But in my discussions with Mr. Gromyko I've emphasized what might broadly be characterized as the human rights aspect of this problem."

Shultz was visited yesterday by Egyptian Foreign Minister Kamal Hassan Ali, who said he transmitted a proposal from the Palestinian Liberation Organization on how best to involve Palestinians in the Middle East peace process.