The National Transportation Safety Board said yesterday it hopes to study whether federal safety standards should be toughened at National Airport and about 20 others.

In a letter to Rep. Frank Wolf (R-Va.), NTSB chairman Jim Burnett said the board "is concerned as to the adequacy of federal safety requirements," particularly those holding that airports need meet only the less stringent airport safety rules that were in effect when they opened. That was 1941 for National.

Wolf, who called for an NTSB study at National after the Jan. 13 Air Florida crash that killed 78 people here, had announced earlier yesterday at a press conference that the board "has agreed to conduct an investigaton as to whether National Airport should be covered by some or all of the latest federal safety regulations," which took effect in 1972.

But NTSB spokesman Barbara Dixon said later that although the study is a "high priority," the problems of reduced staff at the agency and a heavy load of recent accident investigations must be overcome before it can be undertaken. Dixon said the study could begin in the fall if "we can scrape up the resources" and complete a study of the air traffic control system that must be done first.

Wolf, who is running for reelection, said yesterday that he met recently with Burnett and felt he had "a firm commitment" that the study would be done.