The Federal Deposit Insurance Corp. is considering assessing banks an additional $1 billion a year to strengthen the fund that protects depositors when banks fail.

Eroded by the worst string of bank failures since the 1930s, the FDIC bank insurance fund has lost money for two years in a row and the fund's safety margin has dropped to the lowest level ever.

The FDIC had counted on the failures to abate this year and last spring projected that for 1990 the bank insurance fund would break even -- by paying out about as much for losses as it took in from fees charged banks and interest on its invested reserves.

But two weeks ago, FDIC Chairman L. William Seidman told Congress the deposit insurance agency expects to lose another $2 billion this year, which would reduce the fund to about $11 billion. That will leave only 60 cents in reserves for every $100 in federally insured bank deposits, less than half the level that Congress wants the FDIC to maintain.

Industry officials and congressional sources expect the FDIC's board of directors today to set in motion the process of seeking a special increase in fees to replenish the fund. There is widespread speculation in the banking industry that the FDIC will increase the fee, but no clue about whether the FDIC will seek the maximum $1.125 billion rise permitted by law.

The two big banking trade associations said a sharp increase in the deposit insurance assessment would hurt the profitability of banks and make it more difficult for them to raise capital.

Banks now pay an annual fee of 12 cents for every $100 in deposits. The fee is frequently called an "insurance premium" but technically it is a tax the government levies in return for the promise to protect depositors' accounts, even if the insurance fund runs out of money.

Congress raised the deposit insurance tax this year to 12 cents for every $100 of deposits from 8 cents last year. It is scheduled by law to automatically go up to 15 cents per $100 next year.

But that may not be enough to assure the soundness of the fund. Congress last year decided that if the fund declines for two years in a row, the FDIC can raise the insurance fee by as much as 7.5 cents per $100 in deposits per year.

Each additional penny brings in about $250 million a year, so the scheduled 3-cent increase would boost FDIC revenue by $750 million annually. Another $1.125 billion could be brought in if the FDIC ordered the full increase permitted by law.

If the FDIC board approves the full increase, the fee will go to 19.5 cents per $100, an increase of 65 percent from the current rate and almost 250 percent of what banks paid just two years ago.

A spokesman for the American Bankers Association said that group "is committed to do whatever has to be done to keep the bank insurance fund solvent" but has not taken a position on how much the deposit insurance tax should be raised.

Rather than increase the deposit insurance fee, the FDIC ought to consider other ways to raise revenue, the Independent Bankers Association of America (IBAA) urged in a letter sent Friday to FDIC board members. As the representative of small banks, the IBAA said the FDIC ought to make bigger banks pay a greater portion of the cost of deposit insurance by collecting the insurance fee on their foreign deposits and on other special kinds of investments they offer.

Big banks get special benefits, the IBAA argued, because the government considers them "too big to fail" and protects not only deposits of $100,000 or less but virtually all their deposits, including foreign accounts.

The decision will be made by the FDIC board. Beside Seidman, the board includes Robert L. Clarke, comptroller of the currency; Alan Greenspan, chairman of the Federal Reserve Board; Timothy Ryan, director of the Office of Thrift Supervision; and board members C.C. Hope and Donald Hove.