Richard S. Page, Metro's outgoing general manager, warned yesterday that mounting bus and subway costs pose the "single biggest problem" for the Washington area's transit system.

"If I had a disappointment, it would be that there's not yet the kind of firm funding base to support an expanded rail and bus transit operation that there needs to be," Page said during a news conference.

Page's comments were his first since his plans to resign after four years as general manager were disclosed by other officials over the weekend. Page, whose resignation is to be effective May 31, will take over in June as president of the Seattle-based Washington Roundtable, a group formed recently by major Washington State businesses to study economic and social problems.

"I'm not leaving for frustration or disappointment. I'm leaving in order to take on something new," Page said, at the news conference, called to respond to questions about his resignation. "It's really an unusual opportunity that few people are given to step out of one track that you've been in and step over and change careers."

Page did not offer any recommendations yesterday for dealing with Metro's multimillion dollar deficits. In the past, however, he has urged local governments to seek new tax sources to finance public transportation, and he recently asked Metro's board of directors to increase fares to pay for a bigger share of overall transit costs.

The bus and subway system's operating deficits, which must be financed through property and other taxes imposed by local governments, have climbed from $111 million in 1981 to about $200 million under current budget proposals for the fiscal year starting next July 1. Page has warned that the deficits are likely to double again by the fiscal year 1988.

"It's clearly the toughest problem to handle and the most important problem for the board to handle," Page said yesterday.

Page said that his departure may offer the Metro board and other Washington-area officials a new opportunity to reexamine the transit authority's complex structure, an issue that has previously proved controversial. Officials, he said, may also have a chance to clarify ambiguities between the duties assigned to the general manager and those of the board.

"My leaving makes it a little easier for people in the community to look at that question without worrying about the incumbent general manager," Page said.

Page acknowledged that Metro officials face difficulties in getting Washington-area governments to agree on transit policies. "The general manager can get sucked into spending all his time doing that if he's not careful," Page remarked. But he said that such issues played no role in his decision to resign.

"Certainly there's pressure here," he said. "I haven't complained about it. Nor do I feel burned out."

Members of Metro's board of directors plan to meet soon to consider naming an acting general manager and begin seeking a successor to Page. The agency has five assistant general managers, several of whom are regarded as possible candidates for the top position.

Page, 45, currently earns $77,938 a year. Officials here and in Washington state, where Page previously held key government positions, declined to disclose his new salary, though Page acknowledged he would be paid more.