The Department of Veterans Affairs said yesterday that its mistakes in handling government-guaranteed mortgages have cost lenders up to $70 million over the past six years.

Financial institutions were notified Thursday that the agency had discovered a "technical inaccuracy" in the formula used to decide how much of a lender's loss the government should cover when a veteran defaults on a mortgage, said Keith Pedigo, director of the VA's loan guarantee service.

Pedigo said the error has been corrected, and that the losses of financial institutions will be covered. The correct formula has been used on calculations made since Dec. 24, he said.

Lenders' losses could range from $30 million to $70 million, Pedigo estimated. In a letter to lenders, he asked them to document losses and said the "VA will be prepared to honor requests for reimbursement."

Anthony J. Principi, the VA's deputy secretary, said, "We want to be very up front about the error. We plan to do everything we can to identify cases adversely affected by the error and take appropriate action."

Warren Lasko, executive vice president of the Mortgage Bankers Association of America, said some mortgage companies that have gone out of business were pushed over the edge by VA-insured properties that they could not sell quickly enough to recover foreclosure losses. But he applauded the department for moving quickly to reimburse lenders "who were shortchanged."

Some of the houses probably would have been taken back by the VA and resold if the correct formula had been applied and as a result, "there could be litigation" brought by affected lenders, Lasko said.

The department estimated that errors were made in between 8,000 and 12,000 cases over the six-year period, affecting a small percentage of the 235,000 loans that went into default during that period, Pedigo said. Because the mistake was small, only loans on the "razor's edge" of whether they should be kept by the lenders or handed over to the VA resulted in losses to the financial institutions, he said.

The flawed formula also added several hundred dollars to veterans' debts to the government. A veteran who defaults is required to make up any VA losses on a property, but only a fraction of these veterans will ever be able to repay the government, Pedigo said. The VA plans to reimburse the veterans who have overpaid and reduce the debt of the vast majority who have not paid, he said.

The loan program, which has guaranteed more than 13 million loans valued at a total of $360 billion since 1944, assures that a lender will be reimbursed for at least a portion of the losses incurred in a default. After a foreclosure, the VA can either cover the lender's loss and try to get its money back by selling the house, or the department can decide to pay only the guaranteed amount, up to a limit of $36,000, and leave the property with the lender for its disposal. The Deficit Reduction Act of 1984 established a formula the VA is required to use to make this decision.

The VA's mistake made property appear to be worth less than it was.

If the correct formula had been used, the government would have taken over the houses, and, in theory, covered all of its costs when they were sold, Pedigo said. But nearly all of the properties are located in the depressed real estate markets of the Southwest and West, and had lost considerable value by the time they were sold, he said.