President Reagan said yesterday that Soviet leader Mikhail Gorbachev has responded to his invitation for a Washington summit meeting, and other administration officials described the written reply as positive.

In an Oval Office interview, Reagan declined to discuss the contents of Gorbachev's letter but said he is "hopeful" about a summit meeting with the new Soviet leader.

An administration official said Gorbachev, in a letter received last week, endorsed "the idea of a summit" but did not specify a time or place.

Reagan extended the summit invitation in a letter sent with Vice President Bush to the funeral in Moscow last month of Gorbachev's predecessor, Konstantin Chernenko. In the interview, Reagan repeated his desire for the meeting despite the killing March 24 of U.S. Army Maj. Arthur D. Nicholson Jr. in East Germany by a Soviet guard.

"This was a murder, a coldblooded murder," Reagan said, "and it reflects on the difference between the two societies, one that has no regard for human life and one like our own that thinks it's the most important thing.

"And, yes, I want a meeting even more so, to sit down and look someone in the eye and talk to him about what we could do to make sure nothing of this kind happens again," he said.

The official who confirmed the positive nature of Gorbachev's reply said that the killing of Nicholson had "clouded" summit arrangements and that a more detailed Soviet reply about such a meeting is expected.

Reagan said negotiations in Geneva to reduce offensive nuclear weapons are "going forward" despite Soviet objections to his emphasis on missile defense in his Strategic Defense Initiative, often called "Star Wars."

"The [SDI] is purely research, and Mr. [Soviet Foreign Minister Andrei] Gromyko himself said there's no way to control that, that it's not covered by any treaty, and the plain truth of the matter is they've been doing the same kind of research in the same areas and started it before we did," Reagan said.

In the 32-minute interview with The Washington Post, Reagan also contended that disaffection among Nicaraguans with the leftist Sandinista government is increasing and again blamed "rival factions" in the black community for much of the recent violence in South Africa.

Discussing his opposition to the Sandinistas, Reagan said, "I think there are more people who are opposing the regime right now in Nicaragua than actually fought in the revolution against [dictator Anastasio] Somoza.

"And it seems to be growing . . . . You only have to look at the flood of refugees that are escaping from Nicaragua to realize that the people of that country are not happy with that totalitarian regime," he said.

Reagan reiterated his support for antigovernment rebels in Nicaragua, whom he has called "freedom fighters" and "our brothers" but to whom he referred yesterday as "contras," the name applied to them by the Sandinistas.

The president said that, "as long as the people of Nicaragua are still striving for the goals of the revolution that they themselves fought, I think that we're obligated to try and lend them a hand."

The president acknowledged that his policies toward Nicaragua are unpopular with Congress and the public but blamed this on the "very sophisticated lobbying campaign" by the Sandinistas and their Soviet and Cuban backers.

"There has been a disinformation program that is virtually worldwide, and we know that the Soviets and the Cubans have such a disinformation network that is beyond anything that we can match," Reagan said.

White House officials said that the president recently was given a strategy plan for promoting his Central America policies and that it was prepared by communications director Patrick J. Buchanan.

Reagan said he cannot discuss new proposals for persuading Congress to approve $14 million in aid for the Nicaraguan rebels and does not know what he would do if Congress refused to appropriate the money.

"That's something I'd have to face . . . ," he said. "We're not alone in helping them. As a matter of fact, in spite of the polls, there is more and more private support for the contras."

On the recent violence in South Africa, Reagan defended the administration's approach of "constructive engagement," which involves maintaining good relations with South Africa while gradually seeking changes in its policies of racial segregation.

"We think that [what] we're doing is the best, has the best effect, and the most effect of anything that we could do. Just walking away would leave us with no ability to influence them," he said.

Reagan repeated his contention, voiced at a news conference March 21, that rival factions in the South African black community are in part responsible for recent violence.

"Nothing can be solved by violence. And that isn't the answer. But remember, the violence is not just alone stemming from a government putdown of demonstrators," he said.

"You have, in the black community there, you've got rival factions, and the violence is sometimes between them, fighting each other. And we've seen evidence of that, and we've seen murders and some of the 40 deaths have been created in among people without the government participating," he said.

After similar remarks at the news conference, Reagan was sharply criticized by Congressional Black Caucus Chairman Rep. Mickey Leland (D-Tex.), who charged that Reagan had become an "apologist for apartheid," the South African system of racial segregation.

Asked about this criticism, Reagan said his news conference remarks were not intended to condone the government's actions. Reagan said that his critics "maybe have a political bias" and that "they tried to read into it that I was voicing a bias, and I wasn't."

"I was trying to point out just what I did here," he said, adding, "maybe I should have taken more time" to answer the question at the news conference.

"But I was trying to point out that from this being people simply opposed to apartheid against a government that is supporting apartheid, no, it has gone beyond that. There is an element that wants to overthrow the government by violence and is not just limiting its fighting to the government. It is fighting its own fellow citizens and even in the same communities," he said.

Reagan added, "We think apartheid is the main problem that must be resolved, and we're going to continue doing all that we can to encourage the government in its course."

The president was also asked about another controversial remark from that news conference regarding his decision not to visit a Nazi concentration camp site in West Germany in May because an "unnecessary" feeling of guilt has been imposed on today's German population.

The remark provoked criticism in the American Jewish community that Reagan seemed to be suggesting that the Holocaust be forgotten.

Reagan said this was another case where "I guess I should have elaborated more in my answer."

"I have made it very plain and spoken publicly on a number of occasions and will continue to say, we should never forget the Holocaust. We should never forget it in the sense that this must never happen again to any people -- for whatever reason -- in the world."

But Reagan reiterated his view that it would not be right to commemorate the Holocaust during his trip to West Germany because "the bulk of the population . . . were either small children or were not born yet" at the time it occurred.

"And there's no question about it, there are great feelings of guilt even though they were not there to participate in it, of what their nation did," he said, adding that "it just seemed to me that it would be just out of line to emphasize that when I was there as a visitor in their country."

On tax reform, Reagan has yet to submit a detailed proposal to Congress. But he said he envisions one that would have lower rates for corporations and businesses but would raise "generally more money from the corporate sector, but by way of broadening the base . . . there would be an end to some loopholes that probably were never intended to allow large profit-making corporations to escape tax -- totally tax-free for years on end."

The president repeated his view that any compromise on defense spending with Senate Republicans must not touch weapons systems. He said he has not looked at possible Defense Department personnel cuts of 175,000, approved as an option by the Senate Armed Services Committee.

Reagan said comments he has seen and read in the news media that the United States has military "parity" with the Soviet Union are "the most ridiculous thing I've ever heard." He said Moscow "virtually outnumbers us in any type of weapon you want to name . . . . "

On another budget issue, the president became animated as he described a recent conversation with Rep. William V. (Bill) Alexander Jr. (D-Ark.), who asked why Reagan did not submit a balanced budget if he really wants one. Reagan called this "the most hypocritical question I have ever heard" and blamed Democrats for 50 years of deficit spending.

Reagan smiled when asked whether he feels himself growing older in the presidency.

"No, do I look older?" he replied. "I don't feel any older. No, I feel fine."

The president said that being governor of California for eight years had been good training for the presidency even though, "granted, we didn't have a foreign policy."

"For eight years, somebody handed me a piece of paper every night that told me what I was going to be doing the next day . . . ," he said.