The federal agency that regulates savings and loans is pushing ahead on a proposal to allow federally chartered S&Ls in the District to branch into Maryland and Virginia.

The plan would also allow thrifts in Virginia and Maryland to open branches in the District, but thrift industry executives said D.C.-based institutions would be more likely to use new branching privileges to reach the growing number of potential customers in the suburbs.

Congressional aides and thrift industry executives said that by allowing interstate branching in the area, the Federal Home Loan Bank Board would increase the value of thrifts here. That could cut the amount the Federal Savings and Loan Insurance Corp. would have to pay to healthy financial institutions to induce them to buy ailing area thrifts, such as National Permanent Bank in Washington, which has been offered for sale by the bank board.

The bank board included the proposal in a comprehensive package given to the Senate Banking Committee yesterday on what has and should be done by the board and Congress to strengthen the thrift industry and the cash-strapped federal fund that insures it.

Board Chairman Edwin Gray asked Congress to authorize the Federal Home Loan Banks to sell from $8 billion to $10 billion in bonds to provide permanent new funding for the FSLIC, which insures S&Ls.

FSLIC, whose resources have been strained by the record number of thrift failures since 1982, needs $22.5 billion in new funding during the next five years to solve the problems of an estimated 216 troubled institutions with assets of $80 billion, Gray said.

He said money from the bonds and from insurance premiums paid to the FSLIC would supply the funds.

Gray said that within a month the Bank Board and the Treasury hope to introduce legislation to authorize the bonds, which he said would be backed by the earnings of the Home Loan Banks and FSLIC.

Bank Board officials said that if Congress approves the sale, the Federal Home Loan Banks could begin issuing the bonds within 60 days.

The Bank Board said it assumes it will have to pay 20 cents for every $1 of assets it has to merge or sell, bringing to $16 billion the money it will need through 1991 to keep FSLIC healthy. But it has included a 40 percent margin for error, Bank Board officials said, bringing estimated funding needs to the $22.5 billion.

The Bank Board oversees FSLIC and the 12 regional Home Loan Banks, which borrow and lend money to the thrift industry. The stock of the banks, however, is owned by the thrift industry.

The U.S. League of Savings Institutions, a thrift industry lobby, later proposed a similar plan, calling for $23.7 billion to be raised from bonds and premium payments over 10 years. Despite the numerical differences, the league "agrees in principle" with the Bank Board's plan, a league spokesman said.

Gray told Congress it should close the loophole that permits limited service banks, so called non-bank banks. He also suggested that Congress transfer to the bank board the power to define how bank holding companies can operate failed thrifts they acquire. The Federal Reserve Board now has that power.