Soviet President Leonid I. Brezhnev promised today that the Soviet Union will not use nuclear weapons first in any conflicts with other nations, and he challenged the United States to give the world the same pledge about its nuclear arsenal.

Brezhnev's dramatic move was revealed by Soviet Foreign Minister Andrei Gromyko in addressing the U.N. General Assembly's special five-week session here on disarmament.

Gromyko prefaced his speech by reading a message from Brezhnev, and drew a great roar of sustained applause from the delegates when he quoted the Soviet leader as saying:

"The Union of Soviet Socialist Republics assumes an obligation not to be the first to use nuclear weapons.

"This obligation shall become effective immediately, at the moment it is made public from the rostrum of the U.N. General Assembly."

The Soviets have proposed many times that all nuclear powers give up first use of their nuclear weapons, and they have made partial gestures in this direction before. For example, at the last disarmament conference here in 1978 Gromyko pledged that his country would never use nuclear weapons against countries which renounce their production or acquisition and do not keep them within their territory.

However, the pledge today appeared to go further than any past Soviet initiatives, and Moscow's U.N. ambassador, Oleg Troyanovsky, told reporters after Gromyko's speech, "As a solemn undertaking, unilateral on our part, this is the first time it has been announced." The move marks the latest communist thrust in the fencing between Moscow and Washington as they try to marshal support before the resumption of talks on reduction of strategic arms in Geneva on June 29.

Each side has been trying to pressure the other into accepting its views of what the negotiations should cover. They have tried simultaneously to win backing and defuse criticism from the growing body of sentiment in Europe and this country for nuclear disarmament.

In language clearly aimed at putting the United States on the spot before world opinion, the Brezhnev message said the Soviet Union would go ahead with its pledge even though the United States and its allies "make no secret of the fact that not only does their military doctrine not rule out the possibility of the first use of nuclear weapons; it is actually based on this premise."

That charge seems intended to put President Reagan on the defensive in advance of his address to the disarmament session on Thursday. Reagan is expected to repeat his call, made originally on May 9 at Eureka College in Illinois, for both sides to make deep cuts in their arsenals of ground-based missiles.

These are the backbone of the Soviet Union's strategic or long-range nuclear forces, and the Reagan proposals have been rejected by Moscow, most notably in a May 18 speech by Brezhnev, who charged that they were designed to guarantee U.S. "military superiority" over his country.

Today, Brezhnev struck back by calling on the United States and those of its North Atlantic Treaty Organization allies that possess nuclear weapons to make a concession that Reagan administration officials contend would give the Soviets a big advantage over the West.

The United States consistently has rejected past Soviet calls to renounce the first use of nuclear weapons on grounds that it would permit Moscow to use its superior conventional military forces against Western Europe without fear of retaliation from the U.S. "nuclear umbrella."

On April 6, Secretary of State Alexander M. Haig Jr. said that for the United States to give up the first-strike option "would be tantamount to making Europe safe for conventional aggression" and would force the West "to maintain conventional forces at least at the level of the Soviet Union and its Warsaw pact allies."

The Brezhnev message argued that "the world has the right to expect that the decision of the Soviet Union will be followed by reciprocal steps on the part of the other nuclear states."

If the other nuclear powers assume an equally precise and clear obligation not to be the first to use nuclear weapons, that would be tantamount in practice to a ban on nuclear weapons altogether, the Brezhnev message contends.

The message also renewed Soviet calls, which have been rejected by the United States, for a freeze on the nuclear arsenals of both sides "as a first step toward their reduction."

And it said the Soviet Union is "prepared to agree without delay on the complete prohibition of chemical weapons and destruction of their stockpiles."

U.S. officials here publicly sought to downgrade the significance of the Soviet move as a propaganda ploy and a slightly new variation on an old theme. Kenneth Adelman, deputy head of the U.S. mission here, said the statement "was well rehearsed and we've heard it so often that it has a tiresome air to it all."

In his speech, Gromyko spent most of his time detailing disarmament proposals that Moscow has made earlier. He also literally skipped around the world criticizing what he called aggressive U.S. behavior.

In discussing the Middle East, Gromyko sharply attacked what he called Israel's "slaughter" of the Palestinian people in Lebanon. But, while he said that "Israeli troops should be immediately withdrawn from Lebanon," he avoided attaching the term "unconditionally." This was seen here as a sign of continuing moderation and caution by Moscow in opposing Israel's assertions that it will not withdraw from Lebanon until arrangements are made to protect it from attack by Palestinian fighters supported by the Soviets.