Women's National Bank yesterday reported a net loss of $231,000 in 1982 compared with a profit of $240,000 ($2.40 a share) the year before.

The D.C. bank said an increase in loan losses, mainly in its real estate loans, coupled with the costs of opening two branches last year caused the overall loss. Before a gain on securities sales of nearly $130,000, Women's National had a loss of $356,000.

Emily Womach, president and chairman of Women's National, said the bank was surprised by an increase in loan losses near the end of last year and took a loan-loss provision of $140,000 for 1982.

Womach said the bank had to write off as uncollectible $80,000 in loans last year, and she said there are another $45,000 to $50,000 in loans on the bank's list of nonperforming assets.

Womach said it will be difficult for Women's National to turn a profit in 1983. She said the new branches--in Georgetown and on Capitol Hill--probably will be operating at a loss at the end of the year.

The bank has deposits of $12.2 million compared with $11.8 million at the end of 1981.