In what appears to be a classic example of a high-level battle over turf, the Office of Management and budget yesterday squared off with its nearby rival, the Office of Personnel Management, over who controls the size of the Federal work force.

OMB, maker and keeper of the federal budget, denied yesterday that there is an administration plan to fire 125,000 U.S. employes if Congress fails to approve a 5 percent ($3 billion) cut in civil service salaries.

Budget agency officials were furious over reports that staffers at OPM, which sets federal personnel policies, are suggesting that mass dismissals would be the only other way to cut costs if Congress rejects the president's pay cut plan.

But OPM officials stuck by their guns. They say that if $13 billion is to be trimmed from federal personnel costs as part of a three-year deficit reduction plan, it can be done only with a pay cut and freeze, or by reducing the number of workers on the payroll.

Edwin L. Dale Jr., OMB's assistant director for public affairs, said yesterday that "there is absolutely no connection with the budget process we're involved in" and the jobs-cut alternative. "To the extent there are any cuts in federal personnel," Dale said, "they will be done in the usual way, agency by agency. . . .

"If we terminate a program there might be some reduction in personnel," he said. But he maintained that there is no connection between the proposed pay cut and job cuts. "OPM doesn't determine levels of federal employment," the budget agency official said.

Under the president's plan, which would have to be cleared by Congress, federal workers would get the 3 1/2 percent raise scheduled for next month, but would take a 5 percent cut next year. The OPM plan calls for the cut to be made in October at the beginning of the next fiscal year and for pay to be frozen for three years.

But Dale said that the budget, which is still being revised and is not official until the president signs off on it next month, calls for a pay cut in January 1986, and he said that there would be a "resumption of pay increases" the following January.

Patrick Korten, OPM's executive assistant director, said he was "surprised" by the OMB reaction to the jobs-cut alternative, contained in the report on federal compensation being prepared for OPM Director Donald Devine.

Although the report deals mainly with ways to change the way federal salaries are determined, one section of it discussed the alternatives to the 5 percent pay cut.

"Look, clearly we would prefer to make the savings through the pay-cut mechanism," Korten said. "Frankly, folks," he said, "if you want to make the cuts from the federal personnel pie there is only one other way . . . that is by cutting the number of personnel.

"From a management standpoint, we favor making the savings by cutting pay," he said. "The alternative we don't want is to cut people."

Like many federal agencies whose missions sometimes overlap, the OMB and the OMB frequently tangle over policy and methods -- and to determine which agency has the president's ear.

OMB officials are upset that the cut-pay or cut-jobs alternative floated by the personnel agency will backfire with Congress, which may view the alternatives as a form of blackmail.

An OPM official insists that there is "no blackmail involved here. The cuts have to be made and if you can't make them one way and you decide they are necessary, you have to make them another."