The Metro board, trying to stop a worrisome decline in ridership, voted yesterday to postpone any fare increase at least until April. A 6.5 percent fare rise had been tentatively approved for Jan. 1.

The decision is good news for Metro riders, but it probably will mean that taxpayers, already set to provide $177 million this fiscal year in subsidies for the bus and rail system, will find their bills raised by $2 million or more.

The $339 million operating budget the board approved earlier this year assumed fares would go up in January, for the fourth time since July 1980. Yesterday the board voted 5 to 1 to defer that increase, citing fear that raising the price when service quality generally is conceded to be low could alienate passengers and ultimately worsen Metro's financial troubles.

The dissenting vote yesterday was cast by Dorothy Grotos of Virginia. She argued for the January rise, saying that taxpayers deserved some relief from the ever-growing deficits.

Virginia's other voting member, Joseph Alexander, turned aside similar calls from Northern Virginia governments and sided with the District of Columbia and Maryland, which traditionally have been more willing to shoulder subsidies.

The resolution passed yesterday provided that the board would return to the fare issue in November, with April 2 as a possible enactment date. The board remains free to put off the rise past that date.

Before the vote, General Manager Richard S. Page recommended postponing the rise three months longer, until July. Rebuilt -- and hopefully more reliable -- buses will be on the streets by then and an emergency rail maintenance plan under way, he noted. Those and other "get well programs" will improve service and prove to patrons that Metro is worth a higher fare, he said.

Waiting also would give a clearer picture of how much operating aid Metro will get from the federal government this fiscal year, Page said. Bills now before Congress would provide about $19 million but the Reagan administration wants levels to be lower.

January fare rises are especially sensitive to political pressure, he said, because public hearings are held in the fall, just before November elections. For a July increase, hearings would convene in the spring, making them less vulnerable to political considerations, Page said.

The new maintenance programs are meant to help reverse ridership declines, which many Metro officials feel are due in part to poor reliability. Rail is logging about 300,000 rides per weekday, about 30,000 below projections. In July, ridership actually dropped below 1981 figures, despite the opening of three new Red Line stations in Upper Northwest.

Officials had expected a 3 percent fall in use of the bus system due to service cutbacks tied to the new track's opening. Instead, patronage in July was down by more than 8 percent, to around 455,000 rides per day.

To combat the trends, the board has approved programs to rebuild 600 of the fleet's more reliable buses, buy 70 to 80 new buses, tighten maintenance standards generally and build new garages. It is also proceeding with a $44 million plan to replace problem parts on the 300 Metrorail cars.

Page yesterday expressed support for the board's action on fares. "Part of the get well program, I believe, is today's decision to defer a fare increase," he said.

With the exception of Alexander, Virginia's voting and nonvoting board members opposed Page in debate before the decision. Local governments worked out their own budgets assuming that fares would rise, they complained, and now would have to find more money for subsidies.

Virginia alternate member James M. Scott said the decision "disrupts the whole cooperative system that we have developed."

The current budget shows Northern Virginia's share of the subsidy bills as about $48 million, of which only about $20 million is expected to be covered by gasoline taxes and state and federal aid. Local governments in Virginia would have to make up the rest from their general funds.

D.C. and Maryland, in contrast, would have less trouble handling growth in subsidy payments. D.C. has reserved for transit the revenues from certain transportation taxes and fees, while the State of Maryland covers 75 percent of Montgomery and Prince George's counties' costs over a certain level.

In other business, the board:

* Authorized staff to negotiate with the Boston transit system to buy 16 old rail cars to haul trash, farecard machine money and maintenance equipment for Metrorail.

* Awarded a $225,000 contract to Boeing Aerospace Company for a study of the Metrorail control room and operating procedures and authorized bids for a $300,000 study of the subway system's ventilation system. Both studies grew out of the Jan. 13 derailment that killed three people.

* Authorized public hearings into bus route changes in D.C. Metro staff has proposed changes along the "A" routes, as well as the V-3 and W-4 routes.