As Congress mobilizes to cut the defense budget, Pentagon leaders are making the disputed claim that they will save $52.4 billion between now and 1987 through better management.

This new estimate is up almost $1 billion from the $51.5 billion Defense Secretary Caspar W. Weinberger projected in February as the Pentagon unveiled a rearmament program estimated to cost $1.6 trillion over the next five years.

Defense officials said the changes come from sifting through the savings previously claimed by the Army, Navy, Air Force and Marine Corps, rejecting some and adding others to the list.

However, the biggest single savings claimed remains the $23.8 billion from keeping the lid on the pay of federal employes from fiscal 1982 through 1987.

Critics contend this claim is unfair because the pay cap was imposed before President Reagan took office.

"Do you believe this is a legitimate claim by the Department of Defense that this pay cap represents a Department of Defense management initiative?" Sen. Carl Levin (D-Mich.) asked Charles A. Bowsher, head of the congressional watchdog agency, the General Accounting Office, at a Senate Armed Services Committee hearing.

"No, I don't, senator," Bowsher replied. "I think that maybe the administration can claim that, but I don't really think this is a result of a Department of Defense initiative."

Pentagon officials, when asked to justify claiming the $23.8 billion as their saving, said the total stemming from the civilian pay cap projected from fiscal 1982 through 1987 had a rightful place on a list labeled "Economies and Efficiencies" since the lid would save money.

The next biggest saving claimed on the Pentagon's revised list is $15.98 billion in buying some weapons at a lower price and canceling or shrinking 83 others between now and 1987.

Deputy Defense Secretary Frank C. Carlucci said nipping unpromising weapons programs in the bud will save the taxpayers billions.

Again, there are skeptics here, with Levin complaining that the Pentagon has failed to give Congress the details underlying its claimed savings.

Defense Department officials admitted they have been slow in supplying the backup information but said it took time to doublecheck the entries made by the military services.

In listing a $5.6 billion saving in the way it operates the Pentagon, defense leaders projected a reduction of $1.76 billion in the use of consultants and related services.

Levin said this claim does not square with the 91 percent increase earmarked in the administration's defense budget for studies by firms outside the Pentagon.

The administration's list of economies shows $5.5 billion saved by scrapping the Carter administration's plans to revamp the retirement system for military personnel.

The idea was to pay higher benefits in the short run to achieve economies over the long run under a different system. Critics contend the new team at the Pentagon looked at only one side of the equation in claiming those retirement savings in a system that is expected to cost $16.5 billion in fiscal 1983.

One of the veteran Pentagon executives who supervised the compilation of the "Economies and Efficiencies" list agreed that every administration tries to cull wasteful programs. He contended, however, that by directing the military services to document their savings the administration helped make them more cost conscious.

Perhaps in another year--when the nation was not faced with a federal deficit of $100 billion-plus in fiscal 1983 and the Pentagon was not asking for a peacetime record $258 billion--a Defense Department claim of saving $52.4 billion through better management would receive wider acclaim.

Today, however, the congressional emphasis is on reducing the money that the Pentagon is still requesting to rearm the nation, not the additional amount that would be needed if it were not for new team's reforms.