The new chief of the agency that dispenses federal dollars to build and operate mass transportation systems said yesterday that the Carter admintion "is committed to an effective public transit program" but has questions about the rising costs of building subway and operating transit systems.

Richard S. Page, former executive director of Seattle's all-bus transit system, made the comment in a news conference after he was sworn in as administrator of the Urban Mass Transportation Administration, a branch of the Department of Transportation.

Page also said that finding solutions to the financial puzzle facing the Washington Metro authority "is at the top of my agenda." Transportation Secretary Book Adams, Page said, "wants me to meet the Metro staff, board members, and look at the whole thing."

He ducked a question on the Metro's current most burning issue, however - whether or not Adams has committed the federal government to building a "heavy rail" (subway) line from Silver Spring through Wheaton to Glenmont as part of the Metro. "I'm not prepared to comment on that," he said.

Montgomery County Executive James P. Gleason has withheld the county's share of the Metro bus and rail operating subsidies for the first quarter of the current fiscal year until, he says, he gets a commitment from Adams on the Wheaton line.

Page said yesterday that he does not regard the administration's questions about subway building and operational costs for all kinds of systems "as threats . . . I'm concerned, too," he said.

Concern about costs are "questions the public ought to ask . . . Costs have gotten much higher than anybody anticipated in both operations and subsidies." The Washington Metro bus and rail subsidy, for example, is $76 million for this fiscal year.

Page said "yes" when asked if he planned a UMTA campaign to reduce transit costs.

He also praised UMTA's "altenatives analysis" program, which requires that various transit modes - buses, trolleys, etc. - be sutdies for every transportation corridor. Such an analysis is currently under way for about 40 miles of Washington's proposed 100-mile Metro.