The banking industry has tentatively agreed to a plan to pump $10 billion into the dwindling federal fund that insures deposits, industry officials said yesterday.

In order to try to limit future losses to the Federal Deposit Insurance Corp.'s bank insurance fund, the bankers also want to set up a separate $2 billion fund to help finance mergers or acquisitions of failing institutions. The proposal calls for the Federal Reserve to put up the $2 billion.

At the same time, the bankers want the Bush administration to agree that if the government decides to reimburse uninsured depositors when a large bank fails that the Treasury rather than the insurance fund will cover the added cost.

The government on several occasions, under the so-called too-big-to-fail doctrine, has reimbursed all depositors to make sure the failure did not damage the entire financial system. The FDIC guarantees that deposits will be covered only up to $100,000.

The tentative plan was hammered out this week by a broad group of banking interests, including the American Bankers Association, the Independent Bankers Association of America, the Association of Bank Holding Companies, the Consumer Bankers Association and the Association of Reserve City Bankers. Details are expected to be announced early next week.

FDIC Chairman L. William Seidman has estimated that it could run out of money by the end of next year and encounter cash-flow problems before that. Seidman and Treasury Secretary Nicholas F. Brady have been waiting for the industry to come up with a plan to boost the fund, with the banks providing both the initial money and later payments to cover interest on it.

Industry officials involved in the negotiations said banks would be asked voluntarily to lend money to the insurance fund, with the banking groups prepared to twist arms if their members are reluctant.

Cash to cover interest payments and eventually to repay the borrowed money would come from a new premium paid by all banks. The premium would be about 4 cents for each $100 worth of an institution's assets, such as loans, investments, equipment and buildings. Currently, banks pay an annual premium to the insurance fund of 19.5 cents per $100 of insured deposits. The industry decided to assess the new premium against assets rather than insured deposits in order not to hurt smaller banks.

The proposal to use Fed money for the separate $2 billion fund to assist in mergers or acquisitions of failing banks is certain to be controversial. However, the bankers regard as their money about $20 billion worth of cash they are required to keep on deposit at Federal Reserve banks in noninterest-bearing accounts. The $2 billion would come from those reserve balances, but the Fed would receive interest on the money so no taxpayer subsidy would be involved, the bank officials said.