Metro officials, seeking to stem the transit authority's soaring deficits, reached a compromise yesterday on a $363 million budget for the next fiscal year--a financial package hailed as austere by its advocates.

Under the tentative plan, subsidies paid by Washington-area governments to finance Metro's bus and subway system would rise to $201 million, a 7 percent increase over the current fiscal year.

John G. Milliken, a member of Metro's board of directors and vice chairman of the Arlington County Board, described the budget proposal as a breakthrough in local officials' efforts to curb transit costs.

"In terms of turning this around or reversing the trend, I think this begins to do it," said Milliken, who headed a Metro board subcommittee that worked out the compromise.

The plan, for the fiscal year that begins July 1, was approved 7 to 1 by the Metro board's budget committee and is considered likely to be approved by the transit authority's board of directors next week. The action followed weeks of debate among board members and top officials of major Washington-area governments.

The proposed budget represented a compromise between a $384 million package recommended by Metro's outgoing general manager, Richard S. Page, and stiff cuts urged by regional government officials. Page's plan would be trimmed by $21 million.

Page, whose resignation is effective May 31, was described yesterday as troubled by the cuts, but he did not publicly criticize the committee's action.

An outside panel of senior administrative officers from local county and city governments, headed by Fairfax County Executive J. Hamilton Lambert, had proposed bigger cuts, amounting to about $34 million. Similar reductions were urged by a Maryland panel, including officials from Prince George's and Montgomery counties as well as Maryland Secretary of Transportation Lowell K. Bridwell.

The proposed 7 percent increase in local government subsidies to finance transit service would continue to outstrip inflation, which is expected to rise by about 4 to 5 percent next year.

Nevertheless, the increase in Metro's deficit would be far less than in recent years, when it has climbed by more than 20 percent annually.

Page has previously described mounting bus and subway costs as Metro's "single biggest problem" and warned the deficits are likely to double by 1988. He has urged local governments to seek new tax sources to finance public transportation.

The budget cuts have stirred concern, especially among District officials, about possible deterioration in the area's much-criticized bus service.

Milliken said, however, the proposed budget would not jeopardize "critical" transit services. "Metro will have to get along with less," he said.

The budget cuts include a wide range of reductions in personnel and other costs. The recent slowdown in inflation also eased Metro's financial troubles, allowing officials to trim spending for diesel fuel, electric power and wages.