Secretary of State George P. Shultz said yesterday the new leadership of the Soviet Union must make substantive moves to resolve obstacles to improved relations with the United States before it can expect a positive response from the Reagan administration.

"We look for changes in behavior or indications of a willingness to discuss them. We have said we are willing to do so," Shultz said. "I think if you look at the problems that are before us, on the whole they are problems they have created." He said it is therefore up to Moscow to take the first step.

Shultz's statements, a week after Yuri V. Andropov succeeded Leonid I. Brezhnev at the head of the Soviet Communist Party, appeared to demonstrate that the Reagan administration is unlikely to shift from its basic hard-line course just because a new man is at the helm in the Kremlin.

"I hear this word 'signal' all the time . . .but the thing we are looking for is the substance of change in behavior . . . , " Shultz said at a news conference dominated by his assessment of the new Soviet leadership.

His warning against focusing only on positive "mood music" coming from Soviet leaders during the past week came as Soviet Prime Minister Nikolai Tikhonov, citing recent statements by President Reagan, told a group of U.S. business executives visiting Moscow that the new Kremlin leadership is in favor of "normal, or even better, friendly relations with the United States."

The visit by the businessmen is part of a resumption of annual activities of the Soviet-American Trade Council and was encouraged by senior administration officials, including Shultz, before Brezhnev's death. The visit, along with other U.S. actions since Brezhnev died, is being perceived in Moscow as signaling a new tone in U.S.-Soviet relations. Details on Page A25.

Shultz held out the possibility yesterday of some improvement in trade relations with the Soviet Union but made clear that he saw limits to change in the current U.S.-Soviet relationship.

Reaching back to language used often in years past about linkage among various aspects of this relationship, Shultz said, "We must think of our relations in all of their dimensions. While they are not linked in any tight way, certainly they are related to each other."

Citing recent gas pipeline sanctions and the efforts to reach an agreement with major U.S. allies on limiting strategic trade with the Soviet bloc, he added, "That doesn't mean all trade is subject to this kind of examination but in certain critical categories, we believe it must be."

Shultz pointedly cautioned Moscow not to take recent U.S. expressions of a wish for better relations out of context, saying that U.S. policy is based on a realistic assessment "about what is going on -- in terms of military capacity, its use, human rights."

Shultz, who accompanied Vice President Bush in the official U.S. delegation to Brezhnev's funeral, said the signals being sent by Moscow often vary.

"I was of course at the funeral, standing on Red Square for two and a half hours watching what was taking place. Of course, there is the mood music that everybody seems to have focused on, namely the statements the president has made and like statements made on the other side," he said.

"There was other mood music. It was quite startling. But after the body of Mr. Brezhnev was put in the ground and members of the Politburo made up on top of the structure where they stand, it was as though somebody threw a switch and suddenly there was martial music and a long march by of troops. So that was mood music too, I thought.

"We must remember the military strength they have and remember not to in any way allow mood music to delude us or take away from us our own convictions that we must do what is necessary for our own defense."

Shultz's emphasis on the military dimensions of the U.S.-Soviet relationship carried over into areas where he suggested the United States would be looking most closely for signs of a change in Moscow's policy.

"We are engaged in active negotiations for arms reduction in Geneva and Vienna. We are engaged with our European allies, the Soviet Union and others in active discussions in Madrid. So there are three settings where active discussions are going on and where we would welcome movement," he said.

Talks on limiting the use of intercontinental and intermediate-range nuclear weapons are under way in Geneva. Vienna is the site of the long-running negotiations on reduction of conventional forces in Europe. Madrid is the site of the review conference on the Helsinki Accords and has turned into a major forum both for human rights related issues and for "confidence building measures" in the military field.

The Reagan administration also has been hard at work on defense issues in recent weeks with the president expected to announce Monday his decision on the controversial MX missile, just before making a televised address on arms control. That speech is expected to contain a number of proposals on nuclear arms previously aired by Reagan that are separate from the issues being negotiated in Geneva.

In previous discussions of what Washington expects from Moscow for improved ties, Shultz has emphasized regional issues such as Afghanistan and Cambodia as well as placing considerable importance on human rights.

When asked about his omission of these yesterday, he said they "are on my list of things we are concerned about . . . but we don't have talks going on with the Soviets about Afghanistan, for example."

Shultz did say that moves by Moscow in these areas "would be a piece of constructive behavior. When you add up, if things like that occur, they would add up to opportunities for a much improved relationship."