Soviet President Konstantin Chernenko said in an interview today that Soviet-American relations could be improved if the United States would demonstrate a genuine interest in reaching an equitable agreement "at least on one of the essential questions" of arms control.

He singled out four such issues and made it clear that a resolution of "at least some of them" would open the way for the resumption of negotiations on strategic and medium-range nuclear arms.

The four issues included Moscow's proposal to prevent the militarization of outer space, a mutual freeze on nuclear weapons, ratification by the United States of test-ban treaties and a pledge by the United States not to be the first to use nuclear weapons.

Chernenko's proposals for the most part have been advanced previously by the Soviet Union, and they are believed to have been raised again by Soviet Foreign Minister Andrei Gromyko during his recent talks with President Reagan and Secretary of State George P. Shultz, but a senior Soviet official underscored the stress Chernenko had placed on making progress in "some" areas, or even in one of them.

This point was made twice in the first section of the Soviet leader's carefully phrased written response to a series of questions, and a source familiar with Chernenko's intent said it was meant to convey a signal that a "positive" U.S. response in any area could lead to a broader dialogue on arms control, possibly including the resumption of the now-stalled negotiations on strategic or intermediate-range missiles in Geneva.

The 73-year-old Soviet leader was responding to written questions submitted to him by The Washington Post on Thursday and to direct questioning during a 20-minute interview in his Kremlin office today.

Chernenko appeared fit, his handshake was firm and his complexion ruddy during his first interview with a foreign journalist since he became general secretary of the Soviet Communist Party in February.

He described what he called Moscow's persistent efforts to safeguard peace as "the main question for us." He said that, given the nature of nuclear weapons, he believes any American president also must think about that issue.

Soviet policy, he said, will remain unchanged irrespective of the outcome of the U.S. presidential election next month. And, he said, "naturally we would like to see in the face of the American president a partner in this sacred human task -- for peace." Referring to the recent meeting between Reagan and Gromyko in Washington, Chernenko said that "unfortunately" there has been no specific shift in U.S. policies.

But, he said, "if what the president has said about readiness to negotiate is not merely a tactical move, I wish to state that the Soviet Union will not be found wanting." Political observers here noted Chernenko's conciliatory tone and linked his interview to the forthcoming debate on foreign policy between Reagan and Democratic presidential candidate Walter F. Mondale on Sunday.

That the Soviet leader chose to address the American audience at this time can only partly be explained by his desire to inject Moscow's point of view into the Sunday debate, however.

Political observers here believe that Chernenko also wanted to renew his efforts to get a dialogue with the United States underway. He also may have wanted to quiet speculation in the West that he was in ill health and that he may not be in charge of the ruling Kremlin council.

It was Chernenko's first comment on the state of Soviet-American relations following the Reagan-Gromyko meeting. The Soviet leader appeared to articulate his hopes for an improvement in bilateral relations while underscoring his disappointment with the fact that the Washington meeting had not been followed up by what Moscow calls "concrete" and positive steps by the Reagan administration.

The conciliatory language also came after an announcement by Moscow on Saturday that the Soviet Union has begun deploying long-range cruise missiles on its strategic bombers and submarines. That announcement seemed to reflect Moscow's determination to match the U.S. arms buildup in case efforts to revive the arms control process collapse after the U.S. elections.

The Soviet leader outlined the following four areas where "positive" U.S. steps could lead the two countries out of the present impasse: The opening of talks "with a view to working out and concluding an agreement to prevent the militarization of outer space, including complete renunciation of antisatellite systems, with a mutual moratorium to be established from the date of the beginning of the talks on testing and deployment of space weapons." An agreement to freeze the nuclear arsenals of both the United States and the Soviet Union. Ratification by the United States of the "Soviet-American treaties on underground nuclear explosions" signed in 1974 and 1976. Washington's assumption of an obligation not to be the first to use nuclear weapons, an obligation that the Soviets have assumed unilaterally.

All these proposals have been advanced by the Soviet Union during the past few years, and they are believed to have been raised again by Gromyko during his talks with Reagan and Secretary of State George P. Shultz.

"The White House has been silent so far" on these issues, Chernenko said, and therefore there was "no ground to speak" about a positive shift in relations.

Is such a shift possible, Chernenko asked rhetorically in his written answers. "I shall give an unequivocal answer to this question -- yes, it is possible. The resolution of the problems to which I referred earlier would help to bring it about.

"I am convinced that there is no sound alternative at all to a constructive development of Soviet-American relations. At the same time, we do not overlook the fact that we have different social systems and world outlooks.

"But if the responsibility which rests with our two countries is constantly kept in mind, if policy is oriented toward peace and not war, these differences not only do not exclude the search for mutual understanding, they call for it.

"I have already said in the past and I wish to stress it once again: we stand for good relations with the United States, and experience shows that they can be such. This requires a mutual desire to build relations as equals, to mutual benefit and for the good of the cause of peace."

During his conversation, Chernenko sought to emphasize the point that Moscow's search for a resumption of arms control efforts with the United States was not motivated by tactical considerations. He said he thought that "any sober-minded person" could understand it.

"We are doing this not because . . . we like it, but because we have experienced in reality" what a world war means, even without nuclear weapons.

Chernenko said he was "an optimist, but that does not mean an endless optimism since there are limits to everything.

In his written answers, he outlined the Soviet proposals that he said had "run into a blind wall." He appeared pointedly to avoid the mention of the two sets of Geneva nuclear arms talks that collapsed last year when the Soviets pulled out. Moscow contended that the deployment of new U.S. nuclear missiles in Western Europe had changed the strategic balance and made the Geneva talks pointless.

Reaching agreement on the four areas he had singled out, "or at least on some of them, would mean a real shift both in Soviet-American relations and in the international situation as a whole," he said.

Chernenko said that he mentioned "several most pressing problems" linked to curbing the arms race. "There are other important questions which, I believe, the president is well aware of," he said.

"Unsupported by practical deeds, words about readiness to negotiate remain mere words," he added.