Don't dismiss Brezhnev's nuclear pledge

Soviet President Leonid Brezhnev has put President Ronald Reagan on a difficult spot, and the sooner Mr. Reagan gets off it - with credibility - the better.

These are Mr. Brezhnev's simple and carefully chosen words in the statement which Foreign Minister Andrei Gromyko read in his behalf before the United Nations Conference on Disarmament. It is well to keep his exact words in mind:

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

''This obligation will become effective immediately at the moment it is made public from the United Nations General Assembly.''

It is my conviction, as one who has never been ''soft'' on communism nor on Soviet foreign policy, we cannot pass this proposal over lightly or dismiss it unless we want to throw away an opportunity to test Russian good faith.

When the words were pronounced at the UN the press reported that they elicited ''a great roar of sustained applause'' among the delegates of every nation.

As the matter now stands the Soviet offer is overwhelmingly supported by world opinion. If Mr. Reagan stands pat, his position will be overwhelmingly disapproved by world opinion and by much American opinion.

It is understandable that Mr. Reagan should be suspicious that the Soviet leader is making a meaningless promise which will not likely be carried out. There is a basis for such skepticism. In his book detailing his part in representing the White House in many of the Cuban missile crisis negotiations, Robert Kennedy disclosed that the Soviets ''lied to the President 17 times,'' affirming that no missiles had been or were being emplaced in Cuba and keeping this up until photographs disproved these assurances.

It is altogether likely that the Soviets would not believe the US if we matched the Soviet pledge against first use. We wouldn't believe them and they wouldn't believe us.

Is there no way around this mutual disbelief?

I think there is. It is this:

If both sides are committed against the first use of nuclear weapons, there will be no nuclear war. The test as to whether both sides mean what they say is their willingness to act accordingly; namely, to agree to destroy under supervision all nuclear weapons each possesses and build no more.

There is precedent in the past policies of both superpowers.

In 1978 Foreign Minister Gromyko announced that Russia would ''never fire nuclear weapons against countries which renounce their production or acquisition and do not keep them within their territory.''

Why shouldn't Mr. Reagan test the validity of the pledge on no first use by proposing that both sides destroy - under on-site supervision - all nuclear weapons and guarantee they will produce no new nuclear weapons under similar supervision?