President Carter, making a strong appeal for the control and eventual elimination of nuclear weapons, said today that the United States and the Soviet Union "are within sight" of reaching a "significant agreement" limiting strategic nuclear weapons.

Addressing the 32d session of the United Nations General Assembly, the President said such an agreement would limit the total number of strategic weapons each country possessed and would restrict "certain categories of weapons of special concern to each of us."

At a time when attention here was focused on the Middle East, and particularly last weekend's Soviet-American statement on a possible General peace conference, Carter devoted it bulk of his speech to the nuclear issue calling on the assembly to "finally come to terms with this enormous nuclear force and turn it exclusively to beneficial ends."

Carter also made an explicit pledge "on behalf of the United States that we will not use nuclear weapons except in self-defense . . ." He qualified his definition of self-defense to be "in circumstances of an actual nuclear or conventional attack on the United States, our territories or armed forces, or such an attack on our allies."

In the past Presidents have shied away from public declarations that the United States would not launch a first strike with nuclear weapons. President Ford, when asked on June 25, 1975, whether he would consider conducting a first strike, replied: "I don't think it is appropriate for me to discuss at a press conference what our utilization will be of our tactical or strategic weapons."

Carter's carefully qualified statement on the first-strike issue, however, left the question in some degree of ambiguity. White House press secretary Jody Powell initially described the statement as a significant "change in policy" but later corrected himself and said "this country has always maintained that we would not conduct a first nuclear strike."

The President said the United States favors a halt to all nuclear explosions, whatever their purpose, called for a reduction in conventional arms traffic and steps to prevent the expansion of what he called "this terrible club" of nations that already have nuclear weapons.

The speech, which came the day after the expiration of a five-day nuclear arms accord between the United States and the Soviet Union, was clearly an attempt by the President to demonstrate his commitment to ams control and to raise hopes that a new Soviet-American arms agreement can be reached soon. But the basis for Carter's apparent optimism about a new agreement in the strategic arms limitation talks (SALT) with the Soviets was left vague, both in the speech and by American officials here.

Within the last two weeks, the President has held two meetings with Soviet Foreign Minister Andrei A. Gromyko, including an unusual evening session at the White House. At a news conference last week, however, Carter downplayed suggestions that a new SALT agreement was near, saying that while differences between the two nations had been narrowed there was still a long way to go before agreement.

The President did not elaborate on his reference to "certain categories of weapons of special concern ot each of us." However, to the Soviets, the new American cruise missile is the most threatening weapon, while the United States is most concerned with the new generations of Soviet intercontinental missiles with their large payloads.

The five-year SALT I accord that expired Monday established ceilings on the number of land and sea-launched inter-continental missiles. Both the United States and the Soviet Union have pledged to abide by those ceilings while negotiations for a SALT II agreement continue.

The initial Carter administration SALT proposal called for a 25 per cent cut in all strategic nuclear launchers, from 2,400 to between 1,800 and 2,000. This met a hostile reception from the Soviets and any final SALT II accord is expected to involve a much smaller reduction.

But attempting to underscore his commitment to nuclear arms reduction, the President said today that the United States is ready, "on a reciprocal basis" with the Soviets, to reduce its strategic weapons by 10 per cent or 20 per cent, even 50 per cent."

Not once during today's speech did Carter discuss human rights, which has been the centerpiece of his foreign policy and the dominant topic of his first address to the United Nations last March.

He discussed the Middle East situation at some length, taking pains to reaffirm the U.S. commitment to Israel, and touched briefly on the conflict in southern Africa and the attempts to limit military activities in the Indian Ocean.

Noting that the United Nations was founded 32 years ago, "in the cold dawn of the Atomic Age," Carter said that while there is hope for peace the threat posed by nuclear weapons has continued to grow.

"Before the end of this century, a score of nations could possess nuclear weapons," he said. "If this should happen, the world that we leave our children will mock our own hopes for peace."

"Unless we establish a code of inter-national behavior in which the resort to violence becomes increasingly irrelevant to the pursuit of national interests, we will crush the world's dreams for human development and the full flowering of human freedom."

Carter called for an end to all nuclear tests, "no matter what their claimed justification, peaceful or military," and sought to explain his strong stand against nuclear proliferation, which he said he feared many nations did not understand.

"It is a truism that nuclear weapons are a powerful deterrent," he said. "They are a deterrent because they threaten. They could be used for terrorism or blackmail as well as for war. But they threaten not just the intended enemy, they threaten every nation, combatant or non-combatant alike."

In a nuclear age, the President said, nations with nuclear capability have "two solemn obligations" - to meet other nations' "legitimate energy needs" and in so doing "insure that nothing that we export contributes directly or indirectly to the production of nuclear explosives."

Carter's speech marked the beginning of a busy day, crammed with meetings with other foreign leaders but dominated throughout by the tension between the United States and Israel over a Middle East peace conference.

Clearly, the two most important private meetings the President held today were with Egyptian Foreign Minister Ismail Fahmi and Israeli Foreign Minister Moshe Dayan, who met with Carter tonight. American officials said they could provide no details about the meetings.