National Steel Corp., the nation's fourth-largest steel company, came to the rescue of two faltering East Coast savings and loan associations, merging them to create the largest federally chartered savings and loan association in the country, it was announced today.

It was the largest merger of savings and loan associations in history and the first test of a new Federal Home Loan Bank Board policy designed to save troubled S&Ls by permitting them to merge with healthier institutions in other states. The bank board regulates federally chartered savings and loans.

The deal was put together with the aid and encouragement of the Federal Savings and Loan Insurance Corp. National Steel's subsidiary, Citizens Savings and Loan of San Francisco, acquired West Side Federal Savings and Loan of New York and Washington Savings and Loan of Miami. The steel company bought the West Coast S&L in early 1979.

As part of the package, the FSLIC, which insures depositors at savings and loan associations, will indemnify the new association to insure that it does not lose money on the low-yielding mortgages that make up most of the assets at West Side and Washington. The payments from the FSLIC will depend upon the difference between the income generated by the mortages and the cost of obtaining funds.

Industry sources said the price to the FSLIC will be miniscule compared with the losses it would have had to absorb if either or both associations were forced to close down. "The FSLIC got rid of two of its biggest headaches at little cost," according to Jerome I. Baron, who follows savings and loan associations for Merrill Lynch, Pierce, Fenner & Smith, the nation's biggest brokerage firm.

The savings and loan industry has been in deep trouble for more than a year. While most of its assets are long-term, fixed-rate mortgages that yield an average of less than 10 percent, it has been losing its low-cost passbook accounts and having to pay 15 percent or more for new deposits.

West Side, the biggest S&L on the East Coast, has assets of $2.6 billion, and Washington has assets of $1.3 billion. Citizens, which was the most profitable savings and loan in the country last year, has an asset base of $3 billion. Citizens traditionally has middle-class and lower-middle-class savers, according to one industry analyst. Their deposits tend to be more stable than those of more affluent savers.

The new association, which will continue to be known as Citizens, has assets of about $6.8 billion and is the fourth-largest association in the country, behind three state-chartered institutions in California.

Anthony M. Frank, chairman of Citizens, said the associations were losing between $9 million and $10 million a month and that their net worth was near zero before the merger, which was approved by the bank board late Friday.

Citizens and Washington had to convert from state-chartered to federally chartered institutions to enable the bank board to approve the interstate merger.

National Steel also agreed to inject $75 million of capital into the association in three equal annual installments. The first $25 million payment is due next September. Citizens had a net worth of $225 million before the merger. Since the New York and Miami institutions had little, if any, net worth, the new Citizens -- with 136 branches in three states -- will have a net worth of about $225 million, as well.

But with the assets of the new association protected by the federal government, the losses West Side and Washington will incur until interest rates fall will not eat into the net worth of the expanded Citizens.

Frank said he first approahced federal authorities about the possibility of acquiring the two institutionsin May. "It started to get serious in August," he said. He said that West Side was so big he knew that if the bank board were ever to consider trying to merge it with a healthy institution, the board would have to look to an out-of-state association. He said he wanted a Florida savings and loan as well because of the "interaction" between the two states. "Many people spend time in both states. Many New Yorkers have parents living in Florida."

Furthermore, he said, both West Side and Washington had not asset problems except that the assets did not generate enough income to cover the interest costs at the two institutions.