Richard S. Page has decided to resign after four years as general manager of the financially pressed Metro transit system, officials said yesterday.

Page, 45, told members of the agency's board of directors and other high-ranking Metro officials about his decision at a private meeting last week and plans to announce it publicly Monday.

He is expected to take a job as president of the Washington State Business Roundtable, a newly formed Seattle-based organization set up by 30 large businesses in the state. The group will examine public policies involving financial, trade, labor and other economic issues. Page plans to start work in Seattle June 1, Metro officials said.

"It was an offer that he couldn't afford to pass up, apparently," said Fairfax County Supervisor Joseph Alexander, a longtime Metro board member. "Dick Page has taken us through some very difficult times. We're in better shape now than we've ever been."

Page was reported to be returning here late yesterday after a short visit to Seattle and could not immediately be reached for comment.

His new job is in a state where he previously held high-ranking positions. Page was deputy mayor of Seattle in 1970, and he headed the Seattle authority that runs both the area's bus system and sewage treatment facilities from 1974 to 1977. He had been administrator of the federal Urban Mass Transportation Administration for nearly two years before taking over as Metro's third general manager in May 1979.

The salary Page will receive in his new job was not disclosed. He earns about $75,000 a year as Metro general manager.

Metro officials are expected to select an acting general manager soon and to begin searching for a replacement for Page, who succeeded Theodore C. Lutz, now vice president and controller of The Washington Post. Metro's first general manager was Jackson Graham.

Among the most likely candidates to succeed Page, at least temporarily, are Metro's five assistant general managers. Alexander, chairman of the board's budget committee, cited as two possible choices William A. Boleyn, the assistant general manager for finance, and Theodore Weigle, the assistant for transit operations. The three other assistants are Alinda Burke, for public services; John S. Egbert, for construction, and Carmen Turner, for administration.

Page was credited yesterday with helping to bring a new team of highly qualified transit managers to the agency, including Weigle and Burke. "He has done a really top notch job of recruiting new people," said one board member. Page was praised also for showing diplomacy in dealing with Congress and displaying skill in wresting substantial federal aid from the government despite attempts by Reagan administration officials to cut back transit spending severely.

Page, however, has faced increasing difficulty in contending with Metro's contentious board of directors, which includes politicians from Washington-area counties and cities with frequently divergent views. Among the most recent entanglements that have impeded the agency was a protracted dispute over proposals for increasing bus and subway fares, after which the board accepted only some of Page's recommendations.

Alexander described as Page's chief weakness his failure to act firmly, especially in dealing with local governments. "He doesn't like to be visible. He doesn't like to be out in front," said Alexander, characterizing Page as "laid back."

Page's departure comes as the Metro system grapples some of its thorniest financial problems, including proposed cutbacks in federal operating subsidies and new limits on funds from local governments. Last week, the chief administrative officers of major Washington-area governments recommended a $34.4 million cut in Page's proposed $384 million budget for the next fiscal year, a 9 percent reduction that would require stiff curbs on hiring.

The prospect for construction of Metro's proposed 101-mile rail network, now only partly built, have become increasingly uncertain amid rising financial pressures and shifts in federal transit policies.