The Metro board yesterday gave final approval to a $337 million operating budget for fiscal 1983 that assumes that the cost of most rides will rise again by a nickel or more on Jan. 1 next year.

There is considerable opposition to another fare increase among some board members, who fear that a fourth rise in 2 1/2 years would further stagnate Metro's ridership. However, the alternative -- higher subsidy payments from local governments -- also is unpalatable.

The budget already provides for $182 million in operating and debt service aid from state or local governments, 19 percent higher than this year's levels. An additional $14 million in operating aid would come from federal programs.

Member jurisdictions repeatedly have complained that the transit system has grown more dependent on subsidies from local taxpayers in recent years. In fiscal 1983, their subsidy bills will rise unusually fast due to inflation, the start of a phase-out of federal aid and a ballooning debt service schedule.

Without the fare increase that the budget assumes, subsidy payments probably would have to grow beyond the current 52 percent of total expenses. With the fare increase -- projected to raise $4.2 million -- the system's reliance on subsidies would hold steady.

So, barring some unforeseen growth in ridership that would bring in unexpected revenue, the board late this summer will have to take up the politically difficult decision of whether to again raise fares or to finance the deficit by raising subsidy bills.

Prince George's County is on record opposing a fare rise, while Montgomery County's position is less clear, according to Maryland board alternate Carlton Sickles.

D.C. is willing to discuss raising rail fares, according to D.C. board member Thomas Downs. With its population heavily dependent on buses, it does not intend to allow bus fares on routes inside the city to go up.

Virginia officials also have suggested rejecting a fare increase. "A fare increase might be a little bit much at this point," said Virginia board member Joseph Alexander. In fiscal 1981, Metro recorded its first-ever loss in ridership, which was blamed to a large degree on fare increases.

Last December, Metro General Manager Richard S. Page proposed an operating budget of $365 million, $28 million higher than the budget adopted yesterday.

Most of the cut from the proposal was due to lowered projections of how much diesel fuel and cost-of-living raises will cost and the postponement into fiscal 1984 of the opening of new track -- the Blue Line through Alexandria to Huntington and the Yellow Line between Gallery Place and National Airport. The new track would have required hiring of new operators and mechanics.

Metro staff concurred with those cuts but objected to additional ones the board made in programs that Page had said would improve maintenance, reliability and bus cleanliness and help arrest the ridership problem.

The board cut $600,000 from the staff's proposal for general maintenance, $1.8 million from plans to improve bus service through such means as more frequent cleaning and more reserve buses to respond to breakdowns. It cut another $1.2 million by ordering Page to reduce staffing by 51 positions over his proposal.

Some of the new bus programs were approved for selected areas as a test, however.

In other developments yesterday:

Metro announced plans to spend $550,000 to install windows that can be opened in 115 General Motors "advanced design buses" and 41 twin-sectioned articulated buses. The current windows are sealed, causing temperatures to soar when air conditioners fail. Another $850,000 will go to rebuild bus motors and study maintenance and oil spills at garages.

Pylons and Addfare machines will be rearranged and a 10th fare gate installed at Farragut West, which has been criticized as poorly designed for rush-hour crowds it handles, Metro said. Attempts will be made to improve the timing of trains arriving at the station.

The board was told there still is no settlement of a Pennsylvania brake factory strike that is delaying production of cars Metro needs to open the new Blue and Yellow track. Labor and management there tentatively have settled all issues but the fate of 22 strikers fired for alleged violence in connection with the strike