The Metro board, caught in a spiral of rising fares and waning ridership, yesterday formally condemned Reagan administration proposals to make a further 12-percent cut in federal transit aid. Metro is counting on federal programs for $315 million in capital funds and $26 million in operating subsidies this year.

The board unanimously passed a resolution against the cuts one day after a Senate subcommittee marked down Metro's capital allocation, already approved by the House, to $290 million. The Senate version of the bill could also take about $1.5 million out of operating aid for fiscal 1982, the current year, Metro general manager Richard Page told the board.

The Senate bill would reduce total transit spending nationwide to about $3.5 billion, or about 8 percent lower than the House bill's level. Yesterday, Page told the board: "The good news is that it's less than 12 percent," the size of the across-the-board cuts that President Reagan requested last month.

The American Public Transit Association has argued that any additional cuts in federal aid could put some of the country's smaller systems out of business and has urged transit boards to make their views known to Congress forcefully.

A final decision on transit spending could come some time in November, after the full Senate considers the bill and works out a compromise with the House.

Metro's construction schedule for fiscal 1982, part of a four-year plan to have the full 101-mile subway system finished or under construction by 1985, calls for $315 million from the federal treasury. Currently, 37 miles of subway track are operational.

A cut to $290 million would slow construction but probably could be absorbed without completely undoing the four-year building plan, Metro planners say. However, they stress that it remains uncertain how Congress finally would distribute a new round of cuts and whether it would agree to it at all.

While continuing capital programs (on a reduced scale), the administration plans to phase out operating subsidies, which it says have fostered inefficiency, unrealistically low fares and too-generous union contracts. The subsidies now cover about 14 percent of U.S. transit systems' operating costs.

The Metro board, meanwhile, is about to act on a plan to raise the cost of an average ride by 12 percent. In the year ending June 30, the transit system recorded a 3 percent loss in ridership, its first-ever yearly decline, blamed largely on two fare increases during the year. The new fare rise is predicted to cut ridership further, but still bring in $7 million in additional revenues.

In other Metro business yesterday:

* The staff came out against a proposal by D.C. Mayor Marion Barry to let elderly and handicapped people ride buses and subways free in the District. Page cited opposition from Metro's Elderly and Handicapped Advisory Committee, a body of 25 citizens appointed by him. A committee resolution said service, not fares, is the main concern.

* The board was told that Farecard vending machine down-time had decreased significantly since a spare parts shortage was cleared up in recent weeks. In July, morning spot checks typically showed that between 50 and 60 of the 290 machines were out of service or not giving change. This month, the numbers have fluctuated between the 20s and 40s, rail operations head Joe Sheard said later.

* The Rev. Jerry Moore. D.C. board member, proposed that the Alabama Avenue subway station, part of the planned Green Line, be renamed Congress Heights.

* Maintenance figures were released showing that, in every weekday peak-hour in the four weeks ending Sunday, the full complement of 244 cars operated in the subways. In previous periods, breakdowns have often kept car numbers below the scheduled levels, which increases crowding.