President Carter, tying together in a single speech the major elements of his foreign policy, said tonight that he will seek to use the United States' "reservoir of strength" to end the world arms race and nurture human rights around the globe.

In the first foreign policy address of his administration, the President told the permanent representatives to the United Nations that he will not retreat from his emphasis on human rights, which he called "the backbone or our foreign policy."

Specifically rejecting the argument that a nation's treatment of its own citizens is an internal matter that other countries should ignore, Carter said:

"All the signatories of the U.N. charter have pledged themselves to observe and respect basic human rights. Thus, no member of the United Nations can claim that mistreatment of its citizens is solely its responsibilities to review . . . that mistreatment of its citizens is solely its own business. Equally, no member can avoid its responsibilities to review and to speak when torture or unwarranted deprivation of freedom occurs in any part of the world."

The President also went further than he has before in rejecting the so-called concept of "linkage," a Nixon administration formula under which the United States skirted human rights issues in other countries in the interest of progress on other international issues.

"This issue [human rights] is important by itself," Carter said. "It should not block progress on other important matters affecting the security and well-being of our people and of world peace.

"It is obvious," he continued, "that the reduction of tension, the control of nuclear arms, the achievement of harmony in troubled areas of the world, and the provision of food, good health and education will independently contribute to advancing the human condition."

The nationally televised speech in the U.N. General Assembly hall contained no new major foreign policy initiatives by the United States.Instead, Carter used the occasion to develop more fully and to tie together the foreign policy themes and suggestions that have been scattered through his often informal remarks of his brief presidency.

Among those items:

A call for progress in ending the "staggering arms race," perhaps through a relatively quick but limited U.S.-Soviet agreement on some nuclear arms levels, setting aside the more difficult issues until later. In the long run, the President said, "My preference would be for strict controls or even a freeze on new types and generations of weaponry, with a deep reduction in the strategic arms of both sides."

A commitment that the United States will seek to foster "a global economic system which will bring greater prosperity to the peoples of all countries." Specifically, he pledged to support an "open international trading system" that is consistent with U.S. domestic concerns and to consider reaching international economic agreements to stablize commodity prices - an issue of particular concern to the developing nations.

A promise to the American people that he will seek "a more open foreign policy" and will contine to "speak frankly about the policies we intend to pursur . . ."

In his speech to the United Nations, the President touched briefly on a number of sensitive international issues without breaking new ground in terms of U.S. policy.

He pledged U.S. efforts toward achieving majority rule in Southern Africa and noted that, by its rejection this week of the Byrd amendment provisions against U.S. participation in the U.N. boycott of Rhodesian chrome, the U.S. Senate brought the country into compliance with the sanctions "against the illegal regime in Rhodesia."

He mentioned the Middle East only in passing, and said the upcoming May economic summit conference in London must "seek to retrain inflation and begin to find ways of managing our domestic economies for the benefit of the global economy."

In one of his few specific proposals, the President called for a strengthening of the U.N. Commission on Human Rights and pledged U.S. support toward that end. He also said that he will seek Senate ratification of a number of U.N. covenants.

Among these is the U.N. Genocide Convention, adopted by the international body in 1943 but rejected two years later by the U.S. Senate.It is now pending before Congress. Carter also called for U.S. ratification of U.N. covenants on economic, social and cultural rights, and on civil and political rights.

In his remarks on the arms race, Carter said that the race for nuclear superiority between the United States and the Soviet Union has made neither nation secure and he warned that ending that race will be a long and difficult task.

But in a speech that touched on numerous issues, it was the question of human rights that evoked the President's most passionate words, including a reference to his heritage as a son of the American South.

"We in the United States accpet this responsibility [to foster human rights] in the fullest and most constructive sense," he said. "Ours is a commitment, not just a political posture."

"I know perhaps as well as anyone that our ideals in the area of human rights have not always been attained in the United States. But the American people have an abiding commitment to the full realization of these ideals," he continued. "We are determined, therefore, to deal with our deficiencies quickly and openly."

Earlier today, Carter spent 2 1/2 hours moderating a panel discussion on energy issues in the heart of the coal-producing regions of Appalachia in Charleston, W. Va.

Seated around a large table with the President on the state capitol grounds were West Virginia Gov. Jay Rockfeller, Sen. Jemings Randolph (D-W. Va.), United Mine Workers President Arnold Miller, representatives of mining interests, public utilities, conservation, consumer and academic groups and Ed Smith of Gary, W. Va., a coal miner for 40 years for the U.S. Steel Corp.

The participants also included White House energy adviser James R. Schlesinger, Interior Secretary Cecil D. Andrus and Environmental Protection Agency administrator Douglas Costle.

Nothing startling emerged from the discussion. Carter in his remarks, emphasized the need for improved home insulation and unspecified provisions to discourage the consumption of energy during peak demand hours as part of the national energy policy he will unveil on April 20.