The Fairfax County Board of Supervisors, underlining its determination to put a cap on the county's mass transit spending, unanimously voted yesterday to urge Metro to boost its Northern Virginia bus fares by 15 percent and its subway fares by 20 percent.

If the plan is approved by the transit system's board, Northern Virginians will be paying between 30 and 80 cents more each day for round-trip rides into the District of Columbia beginning July 1.

Approval of the entire request is not certain. Metro likely will go along with the increase in Virginia bus fares, but District of Columbia opposition is likely to reduce the size of the suggested subway increase, according to Metro spokeswoman Marilyn Dicus. Metro officials are supposed to reach agreement on a new fare schedule by May 22, she said.

"The District has always wanted to have lower rail fares than Virginia officials want," she said, "so there will have to be some kind of compromise."

Fairfax officials said their proposal, which would generate an additional $1.4 million in Metro revenues annually, is needed if the Virginia suburbs are to hold their own against rising mass transit costs. Alexandria and Arlington officials have lent their informal support to the Fairfax proposal. a

"The primary reason for the increase is simply to keep some kind of relationship between the increasing costs of providing service and our revenues," said Fairfax Transportation Director Shiva K Pant. "People sometimes don't remember that even with the same amount of service each year, our cost goes up considerably," the result of rising labor costs.

Pant said the fare increases will ensure that the county continues to recapture approximately 39 percent of its Metro costs through the fare box.

The decision by the Fairfax board is only the latest development in a recent trend by Northern Virginia jurisdictions toward insisting that Metro hold down costs. Arlington, Alexandria and Fairfax County all have made substantial cuts in funds Metro has requested from them for its 1981 operations.

Under the Fairfax proposal approval yesterday, commuters traveling between Virginia and the District of Columbia by bus during off-peak hours would be hardest hit fare increases. They would pay 37.5 percent more for their rides, or up to 80 cents more for commuters traveling from areas beyond the Capital Beltway.

Affected least would be Arlington and Alexandria commuters who transfer between the subway and the bus at Rosslyn. They would add 30 cents or 14 percent to their present daily commuting fare of $2.15.

Fairfax County commuters who use both bus and rail would find that their daily cost had risen between 50 and 60 cents, ending with a daily fare of between $3.35 and $3.65 depending on the route and transfer points.

Supervisor Marie B. Travesky (R-Springfield) said the board's approval of the plan, which came with no public discussion, was "totally in line" with sentiments expressed by officials in the other Northern Virginian suburbs.

She said the proposed fare increases for the subway are higher than those proposed for buses because the subway "is a very attractive form of transportation. It comes closer to paying for itself, and we believe it really should."