In a dramatic attempt to gain a substantial foothold in the transcontinental airline market, World Airways yesterday lowered its fare between Baltimore and the West Coast to $70 each way for a one-month period beginning next Tuesday.

Since Feb. 27, when World resumed its flights after a lengthy strike, it has been charging $193 to Los Angeles and $202 to San Francisco.

World's low promotional fares, including a Baltimore-Hawaii fare of $140 each way and Newark-West Coast fares of $70 each way, already have been approved by the Civil Aeronautics Board.

The fares apply to every seat on every World flight without advance-purchase or minimum - maximum-stay requirements. The tickets are nonrefundable, however.

"You'll never have to play some boondoggle bingo game to get a decent flight at a reasonable fare from World Airways," Edward J. Daly, World's president and chairman, said yesterday in an obvious reference to the games some of the other airlines have promoted in an attempt to gain customers.

Daly also appealed to the public to support World and the role it has played in fostering fare competition. Low air fares won't be available if World can be driven from the market, he contended, noting that the major cross-country airlines eliminated their sharp discounts last year after World was grounded.