Even as other federal agencies are laying employes off, the military services have asked the Reagan administration to add 72,000 civilians to the Pentagon payroll over the next five years to help carry out the president's rearmament program.

The request already has upset some White House budget officials who warn that defense spending must be curbed if President Reagan is to have any hope of balancing the federal budget by 1984, as promised.

Lawrence Korb, the Pentagon's manpower chief, confirmed yesterday that the services have indeed submitted requests to increase their civilian workforces by about 72,000 during the five year period fiscal 1983 through 1987. Administration officials will start debating that request today or next week, he added.

The Defense Department up to now has succeeded in adding to its civilian payroll, which went from 990,000 in fiscal 1980 to 1,025,000 in fiscal 1982, Korb said. One argument for doing this while other government departments were forced to retrench was that civilians free officers and soldiers for strictly military duties. The services have had trouble, under the all-volunteer regime that has been in effect since 1973, in recruiting and keeping all the uniformed personnel they need, particularly those with certain needed skills.

Defense Secretary Caspar W. Weinberger has said that an expanded civilian work force is essential to carrying out his charter from the president "to rearm America." The Reagan-Weinberger blueprint calls for adding about 200,000 to today's standing force of 2.1 million soldiers, sailors, airmen and Marines without resorting to the draft.

The administration's stated rationale for such a big increase is that the United States must prepare to fight the Soviets and/or their surrogates in several places at once thousands of miles apart. Weinberger has refused to put a limit on how many wars the United States must be prepared to fight at once.

Also, in his recent secret guidance sent to the military services, he said that any future non-nuclear war may go on for years. Therefore, he added, the services must determine how to gear up the nation's defense industry to fill an eight-fold increase in orders in a period of tension and absorb half the gross national product in a national emergency.

Although Reagan has sided with Weinberger in past arguments over how much is enough for defense, there is growing concern among White House budget officials that Pentagon spending is getting out of hand. Deputy Defense Secretary Frank C. Carlucci has publicly acknowledged that additions to former president Carter's last two defense budgets are costing $10 billion more than first anticipated in bills falling due in 1983.

White House Budget Director David A. Stockman has been losing to Weinberger and Secretary of State Alexander M. Haig Jr. in his effort to reduce defense spending, sources said. But these sources added that he expects to pick up strength within the next few months from other Cabinet members because they have been asked to submit lists of even deeper cuts in their departments by September. The theory is that these Cabinet members will agree it is high time for the Defense Department to feel the budget ax.

In case Stockman wins this on-going argument or reductions are required for other reasons, the military services in submitting their budgets to Weinberger for fiscal 1983 through 1987 have been asked to list what they would leave out if ordered to cut their total requests by 5 percent.

It is in this context that the request for the extra 72,000 civilians will be fought out.