The Reagan administration yesterday welcomed the tone but reacted cautiously to the substance of Soviet President Konstantin U. Chernenko's statement Tuesday in an interview with The Washington Post that Soviet-American relations could be improved if the United States would demonstrate genuine interest in reaching agreement on at least one of four arms-control proposals.

"To the extent the interview conveys a more positive tone, it provides a basis for hope," said Robert C. McFarlane, the president's national security affairs adviser. "From a substantive point of view, it provides nothing new."

However, he added that administration officials believe the Soviets are still "chewing over" ideas for improving superpower relations advanced by President Reagan in his Sept. 28 White House meeting with Soviet Foreign Minister Andrei A. Gromyko, and said that Chernenko's comments could be a sign of Soviet willingness to explore them further after the presidential election.

Vice President Bush, speaking yesterday to the Commonwealth Club in San Francisco, gave a similar response, calling Chernenko's statements "a positive sign."

"What is important in the Chernenko interview is the tone of its rhetoric," Bush said. "The tone was not confrontational, and there will be a balanced response to it."

Advisers to both Reagan and his Democratic opponent, Walter F. Mondale, have said they thought that the interview, the first Chernenko has given a foreign journalist since he became Soviet leader in February, was motivated at least in part by a desire to push arms-control issues to the forefront in advance of Sunday's foreign-policy debate by Reagan and Mondale.

With this in mind, strategists in both political camps were wary of overinterpreting Chernenko's statements. However, an administration official said that "despite the obvious political overtones" of Chernenko's comments, there was also the possibility that his remarks could be a prelude to a serious attempt at nuclear arms negotiations.

Chernenko listed four issues and made it clear that a resolution of "at least some of them" could open the way for resuming negotiations on strategic and medium-range missiles.

The four issues are Moscow's proposal to prevent the militarization of outer space, a freeze on nuclear arsenals, U.S. ratification of previously negotiated test-ban treaties, and a U.S. pledge of no first use of nuclear weapons.

In his first comments on the subject, Mondale yesterday took a gingerly approach. "It is up to the administration to respond to this initiative and ascertain what it means," said a statement issued by Mondale's headquarters here. "As with any Soviet proposal, you have to look at the fine print, and some of these ideas -- such as no first use -- are clearly not in our interest. We have only one president at a time, and it is up to Mr. Reagan to explore this proposal seriously and determine its significance."

Democratic vice-presidential nominee Geraldine A. Ferraro, interviewed last night on ABC News "Nightline," said the Democrats were "not sure" what the Soviet leader meant when he included a nuclear freeze as one of the is- sues for resolution. The Democrats have pledged support for such a freeze.

Under questioning, Ferraro said a freeze is "not going to stop everything." Asked how a freeze could be verified, she said, "We would freeze only that which is verifiable."

Administration officials, speaking on condition that they not be identified, discounted the importance of both the no-first-use pledge and the nuclear-freeze proposal as reiterations of Soviet positions.

But privately they were intrigued by the suggestion that the Soviets might resume other negotiations if the administration agreed to ratification of the 1974 and 1976 test-ban treaties. Reagan has opposed ratification because of Soviet opposition to on-site verification, a position Chernenko reiterated. But one U.S. official suggested that the United States could modify its ratification stance if agreement is reached on verification by other means.

If this happened, the official continued, "it is conceivable" that the Soviets might have provided themselves an opening to resume bargaining on nuclear arms reductions.

The official administration response yesterday gave no sign of any change in U.S. positions.

White House spokesman Larry Speakes took the unusual step of appearing before cameras at the daily White House briefing to read a response carefully worked out with Reagan's foreign policy advisers. The statement, though couched in unprovocative terms, blamed the Soviets for the current arms-control stalemate and mildly rebuked Chernenko for making his proposals in a newspaper interview.

"President Chernenko has stated that improvements in the U.S.-Soviet relationship depend on deeds, not words," it said. "We agree. When the Soviet Union is prepared to move from public exchanges to private negotiations and concrete agreements, they will find us ready."

"We agree with President Chernenko that there is no sound alternative to constructive development in relations between our two countries," the statement also said. "We are pleased to see the emphasis he puts on positive possibilities for U.S.-Soviet relations. We will be studying his remarks carefully and, as was agreed during Deputy Prime Minister Gromyko's recent meeting with President Reagan, we will be pursuing our dialogue with the Soviet Union and exploring the possibilities for progress . . . ."

Speakes said Reagan "has repeatedly demonstrated that we are ready for cooperation with the Soviet Union." He gave several examples and said that "this summer we accepted a Soviet proposal to begin space arms-control negotiations in Vienna without preconditions."

However, Chernenko in his interview again blamed the United States for failing to undertake these negotiations, which the Reagan administration wanted to extend to discussions on limiting nuclear weapons. Mondale has criticized Reagan for insisting on what he has described as a precondition.