President Carter today laid out goals of broader cooperation with the Soviet Union based on "enlightened self-interest" he said represent the framework of his Soviet foreign policy initiatives.

He emphasized, however, in a speech conciliatory in some places and tough in others, that "the basis for a complete mutual trust does not yet exist." He pledged that if a strategic arms limitation agreement cannot be reached, "there should be no doubt that the United States can and will do what it must to protect our security and insure the adequacy of our strategic posture."

In his first major speech in the South since he took office, Carter said his decision to speed up development of the cruise missile was "aimed at compensating for the growing threat" presented by a buildup of Soviet offensive strategic weapons.

If Soviet threats to U.S. deterrent forces "can be controlled, and I believe they can, we are prepared to limit our strategic programs," he said. That issue has been a major sticking point in the current and past SALT talks.

Carter said military competition with the Soviet Union "is still critical, because it does involve issues which could lead to war," but it cannot be "our sole preoccupation to the exclusion of other issues which also concern us both."

He said his negotiations with the Soviet Union "will be guided by a vision of a gentler, freer and more bountiful world," but with "no illusions . . . "

The 30-minute speech, which Carter did not whip into final shape until a few hours before he left Washington, was the first time he has publicly set forth the goals of the foreign policy he hopes to conduct with the Soviet Union.

It appeared designed primarily to generate support among the American people, and also to reinforce signals the administration has been sending to Soviet leaders. The administration has been considering for weeks the best format for the President to explain his views.

"It is not a question of a 'hard' policy or a 'soft' policy," the President said, "but of a clear-eyed recognitions of how most effectively to protect our security and to create . . . a more reciprocal, realistic and an ultimately more productive basis . . . " for relationships between the two superpowers.

"What matters ultimately," he said, "is whether we can create a relationship of cooperation that will be rooted in the national interests of both sides. We shape our own policies to accomodate the changing world, and we hope the Soviets will do the same."

Major themes which the President chose to detail before the 31st annual Southern Legislative Conference of the Council of State Governments at Charleston's Municipal Auditorium included:

"The whole history of Soviet-American relations teaches us that we will be missed if we base our long-range policies on the mood of the moment, whether that mood is euphoric or grim . . . On balance, the trend in the last third of the century has been positive."

"The profound differences in what our two governments believe about freedom and power and the inner lives of human beings are likely to remain, and so are other elements of competition between the United States and the Soviet Union . . . but it is also true that our two countries share many important, overlapping interests. Our job is to explore those interests and use them to enlarge the areas of cooperation between us . . . "

A strategic arms limitation agreement . . . which reflects just the lowest common denominator that can be agreed upon will only create an illusion of progress and, eventually, a backlash against the entire arms control process."

He said there have been "some negative comments from the Soviet side about SALT and about our more general relations." Part of the Soviet leaders' attitude, he said, "may be due to their apparent - and incorrect - belief that our concern for human rights is aimed specifically at them or is an attack on their vital interests.

"There are no hidden meanings in our commitment to human rights . . . to be policy is exactly what it appears to be: the positive and sincere expression of our deepest beliefs as a people."

That policy is addressed "to all countries equally, including our own," Carter said, "and it is specifically not designed to heat up the arms race or bring back the Cold War."

Soviet leader Leonid I. Brezhev "said something very interesting recently," the President said: "'it is our belief, our firm belief,' he said [quoting Brezhnev], "that realism in politics and the will for detente and progress will ultimately triumph and mankind will be able to step into the 21st century in conditions of peace, stable as never before.'"

"I see no hidden meaning in that," Carter said. "I credit its sincerity. And I express the same hope and belief."

Carter laced his speech with references to his Southern heritage. He said he was proud to talk about "the problems and the hopes that we, as Southerners, and as Americans, all share."

He noted. "We in the South have also felt, perhaps more directly than many others, some of the rapid changes in the modern age. More and more our daily lives are shaped by events in other cities, decisions in other states, tensions in other parts of the world."

The theme of "interdependence" was also a major feature of this speech.

"Both the United States and the Soviet Union have learned that our countries and our peoples, in spite of great resources, are not all powerful . . . This world, no matter how technology has shrunk its distances, is nevertheless too large and too varied to come under the sway of either one or two superpowers."