The Pentagon wants to spend an additional $600 million to build a more powerful warhead for the MX missile that neither the Air Force nor the Office of Management and Budget wanted, according to administration sources.

Though each of the new warheads will have increased explosive power, their larger size will reduce the number that each MX can carry from 10 to either nine or eight, according to weapons experts.

The Defense Department "is planning to spend a great deal of money for a marginal gain," was the way one Reagan administration official put it.

A Pentagon official involved in the decision, who asked not to be identified, countered that various factors were involved in the decision and that the final "cost to the taxpayers will be a wash" with the new weapon.

However, according to sources in the nuclear weapons building community, more than just a warhead was involved in the decision, which has been in an on-and-off state for several months.

Some say a longstanding controversy between the nation's two nuclear weapons laboratories was a key issue.

The new warhead was designed at Lawrence Livermore Laboratory in California, home of Dr. Edward Teller and other scientists who advocated bigger nuclear weapons. All the new, major strategic weapons systems of the 1960s were built at Lawrence Livermore but this is the first strategic weapon contract it has won in more than 10 years.

The smaller MX warhead that is being replaced--the Mark 12A--was developed at the Los Alamos Scientific Laboratory in New Mexico, which had beaten out Livermore in designing the current generation of strategic weapons, including submarine-launched, air- and land-based ICBMs.

Adding to the controversy is the fact that the decision for the Livermore warhead was pushed through the Pentagon by an alumnus of Livermore, Dr. James P. Wade Jr., deputy undersecretary of defense for research and engineering.

Wade has critics and defenders in the current controversy.

"I don't believe Wade did it just for Livermore . . . . It was a compromise decision based on pulling and tugging. It's neither right nor wrong," one leading scientist in weapons development said yesterday.

One argument Wade reportedly made was that if the United States were to run short of enriched uranium needed to make both warheads, the Livermore version would use less because of its design--if its size were reduced to that of the Mark 12A.

A Wade critic called that argument "specious," noting that Wade, among others, was pushing for additional Navy nuclear weapons that if approved would be the cause of any nuclear materials shortage.

Another argument for the Livermore warhead was that if the MX is carried on a long-flying aircraft, it will need a larger yield because it won't be as accurate as it would based in a silo.

Under previous plans of the Carter and Reagan administrations, the MX was to carry 10 Mark 12As, each of which delivers the explosive power of 340 kilotons. The bomb that destroyed Hiroshima was 12.5 kilotons.

The Mark 12A is already in production since it is being put on 300 of the current Minuteman III missiles now deployed to increase their explosive power. The original plan was to keep the Mark 12A production line going and turn out additional ones for the MX.

For the Air Force and OMB this was the most economical course. The General Electric Co., which builds the Mark 12A reentry vehicle, is lobbying on Capitol Hill against the new, larger warhead.

The new warhead, which has undergone some flight testing, still needs an estimated $600 million more to be developed as a production weapon, according to administration sources. An important phase of warhead development is producing the correct size and shape for the reentry vehicle and then testing it, putting it on missiles and firing them from silos in California to target areas several thousand miles away in the Marshall Islands.