The White House budget office is feuding with savings and loan regulators over who is to blame for the government's rapidly mounting cost of shutting hundreds of insolvent S&Ls.

The Federal Home Loan Bank Board, the federal agency that regulates S&Ls, blames the Office of Management and Budget and other government agencies for limiting the number of S&L examiners and supervisors the bank board has been able to hire.

An employe shortage permitted fraud and mismanagement to go undetected and to undermine the health of many S&Ls, bank board officials say.

As a result, scores of S&Ls must be closed that otherwise might have survived the pressure of depressed energy and real estate prices, the regulators say. Shutting the institutions will add billions of dollars to the bank board's expenses.

OMB officials yesterday delivered a letter to House and Senate members denying it is at fault. In fact, the bank board "has not been able to use all the staff . . . authorized by OMB" for the past four years, OMB officials said.

The longstanding dispute was stirred up again as the House and Senate banking committees began meeting yesterday to reconcile banking bills recently passed by the two chambers. The Senate bill includes a provision to eliminate OMB's budgetary oversight of the bank board's and other government agencies' expenditures to shut failed S&Ls and commercial banks.

So far the OMB controversy has been overshadowed by other banking issues that many House and Senate conferees consider more pressing.

In the next several days conferees hope to agree on how many billions of dollars to pump into the insolvent Federal Savings and Loan Insurance Corp., the bank board division that insures deposits at S&Ls, and on whether to close a loophole in federal banking law that enables companies from a variety of industries to own banks.

The so-called nonbank bank loophole has allowed giant retailers, insurance companies and securities brokerage houses to sell banking products. Many banking lobbyists say that if the loophole is not closed in this session of Congress, it is unlikely ever to be closed.

The conferees also must try to agree on whether to freeze banks' expansion into insurance and securities underwriting and on whether to limit the time it takes banks to clear checks drawn on other institutions.

The bank board has been plagued for years with high turnover and vacancies among key staff. The condition has led to higher costs that in turn have helped make FSLIC insolvent, bank board officals said.

Bank board officials say the fault rests with OMB, the Office of Personnel Management and Congress. On national television Friday, for example, bank board lawyer William Black blamed his agency's staffing shortages on the shortsightedness of those who have tried to reduce salaries and the number of employes at the bank board and other federal agencies.

In the long run the policy proved to be "penny wise and pound foolish," he said.

But the OMB told House and Senate committees it had "reviewed actual staffing levels that reflected the bank board's inability to hire up within the previous year," OMB Associate Director Carol T. Crawford said in the letter. Based on that review, OBM has adjusted the bank board's "overly optimistic projections" of how many employes it needs to hire in a given year.

A management study requested by the bank board and completed last fall reached a similar conclusion, noting that the bank board fund that insures deposits at S&Ls was mismanaged in part because key jobs at the agency had been left vacant for months at a time.

OMB argues that even if Congress decides to sever OMB's oversight of government outlays to shut S&Ls and banks, the bank board's staffing problem will not be solved.

"Exempting the banking agencies from the apportionment process will not resolve staffing difficulties," the letter said. "Congressionally enacted . . . expense limitations determine staffing levels."