The Metro board adjourned yesterday without adopting a budget to run the bus and subway system after July 1 because of District of Columbia opposition to a fare increase needed to balance the budget.

The lack of action precipitates another of those Metro financial crises and leaves unanswered such questions as whether Metro subway service will be extended into the evenings and on Saturdays. The budget calls for such an extension beginning in November.

At the same time, the budget problem brings into sharp focus the enormous political difficulty District of Columbia politicians have had since last July 1, when the rush-hour Metro bus fare jumped 10 cents and transfers were eliminated between bus and subway.

The result was a sudden increase of as much as $1 a day in round-trip public transit costs for some D.C. resident. It was the first fare increase in the District in seven years.

"Very frankly, for us, it's politically impossible to raise fares," said Metro board member Jerry A. Moore of the D.C. City Council. "I don't know how this it going to be worked out, but that is the District position."

All the suburban jurisdictions that have reviewed the Metro budget have approved it in principle. Both Arlington and Alexandria have asked for even higher fare increases than the 7 percent increase called for in the budget. That increase would be effective next July 1, on the eve of what is expected to be intense campaigning in the District City Council and moyoral races.

In the past, the Metro board has adopted budgets that presumed fare increases, then ducked the fare increase. There is opposition to taking that course again.

In the current fiscal year, Metro is running a $4-million revenue shortfall because there was no suburban bus fare increase in July and because the subway fare was set at a lower rate that originally planned. There was a suburban bus fare increase last March. The immediate effect was that about 5,000 persons a day quit riding the buses and revenues went up.

The board deferred action on the budget for one week after a 15-minute recess that was occupied with numerous small caucuses in various corners of the board room. When the board returned to session, the deferral was announced.

After the meeting, board Chairman Joseph S. Wholey, of Arlington County, said "the board is unwilling to approve a budget unless we know in fairly concrete terms what portion is going to come from the farebox and what portion from the taxpayers."

There appeared to be general agreement on the concept of extending subway service from 8 to 11 p.m. weekdays and adding 14 hours of service on Saturdays.

THe budget before the board also includes the continued use of tickets and tokens, something the Metro budget committee had sought to eliminate. The total proposed budget, bus and rail, is $195.1 million, a 14 percent increase over the the current budget of $171.2 million.

The budget also presumes that the total subsidy for bus and rail will be $102.2 million, assuming the fare increase. If there is no fare increase, the subsidy would increase by $6 million. The Maryland and Virginia subsurbs provide most of the subsidy from property taxes, which is becoming politically unacceptable for their politicians. The District has both the property tax and the income tax as possible sources of transit subsidy.

If it were simply a question of bus fare, there would be no problem. The buses are becoming more and more local in nature and bus fare have always been set at essentially separate levels for each of the three major jurisdictions.

Both Maryland and Virginia have adopted zoned bus fares - higher charges for longer rides - while the District has maintained a single-fare bus structure; the same fare regardless of the distance.

The result has been a complicated bus fare system for the traveler crossing state lines, but one controlled and budgeted largely by the independent actions of the local jurisdictions. The Metro board went along with the wishes of the locals.

It is impossible to run a railroad that way. When the subway's Blue Line opened last July 1, formulas had to be struck to allocate the operating losses among the three jurisdictions and the fares had to be set the same for everyone.

The fare structure is based on distance traveled, regardless of whether it is traveled in Virginia, Maryland or the District. Thus, any fare structure must be perceived as fair by all sides. The Metro board went to the 11th hour before adopting the present fare structure and subsidy allocation formula.

The problem for D.C. residents was twofold. First, on July 1 the bus fare increased during rush hour from 40 cents to 50 cents. Second, many buses were cut off a new Blue Line Metro stations. There, the rider had to pay a separate subway fare, bringing the total to 90 cents for one trip.

To ease the cost of the return trip, Metro created a transfer system that lets riders switch from the train back to the bus free of charge (except in Virginia). That makes the total round trip for the D.C. resident about $1.30. Before the subway, that trip cost 80 cents.

There's a catch, however, for those who must take first a bus, then the train, then a second bus to complete a one-way trip - and many D.C. residents are in that category. Because it is impossible to transfer from bus to train, people in that category never get the round-trip fare break. Thus they have two full bus fares of 50 cents each two train of 40 cents each, for a total trip of $1.80.

Before the Blue Line, the whole trip could be made for 80 cents. This problem was known to both D.C. and subsurban members of the Metro board last summer. They promised to find a cure when they adopted the subway fare table last summer; they have never done so. That is at the heart of the D.C. insistence on no fare increase.

There are proposals for transit pass that would permit a Metro customer to buy a two-week pass for unlimited bus use and limited rail use. That pass would solve the above problems, but it would also cause an estimate increase in the deficit of about $2 million that must be made up somewhere. That is the suburban position.

There also are the other charges of who is subsidizing whom. District residents testify at Metro hearings that they are carrying the long-distance suburban riders on their taxpaying backs Suburban riders, who have much higher bus fare, testify that subsurbs. The complicated Metro cost formulas are supposed to equalize that. There are arguments about whether they do.

There is room for compromise, most board members agree. It will doubtless involve some kind of transit pass and suburban bus fare increase.

"I don't sense a disagreement on what the level of service will be," Wholey said. "We will keep talking among ourselves."