The Fairfax County Board of Supervisors yesterday endorsed a controversial new hospital for the fast-growing western section of the county, setting the stage for an intense battle for health-care customers between the nonprofit association that long has controlled the county's hospitals and for-profit hospitals planning to locate there.

The board voted 7 to 1 to allow the private Fairfax Hospital Association to move ahead with plans to build a 160-bed hospital in the burgeoning Fair Oaks area near the intersection of state Rte. 50 and Interstate 66.

The board tentatively approved plans for the proposed hospital, despite warnings from the county Health Advisory Board that most hospitals in Northern Virginia already are severely underused and predictions from the county's planning commission that the hospital would create massive traffic congestion in the surrounding residential neighborhood.

Supervisor Martha V. Pennino, the representative of the Centreville district, where the new facility would be located, vehemently opposed the project, citing a second hospital the board soon will be asked to approve for the Reston area, also part of her district.

"The board is being very shortsighted," said Pennino, who long has campaigned to bring a hospital to Reston, "knowing full well there is going to be one hospital a short distance away."

One of the association's potential rivals, the private, for-profit Hospital Corp. of America, has proposed building a 127-bed facility in the Reston area. It will need a zoning variance for its hospital, the same issue that brought the association before the board yesterday.

Both proposed hospitals, expected to cost more than $30 million each, have stirred controversy among state and local officials attempting to grapple with increasing problems in filling existing hospital beds. Fairfax Hospital Association has proposed closing its Commonwealth Hospital in Fairfax City when its new Fair Oaks facility is completed, despite objections from city officials.

The association's competitor, HCA, has said it will close its 127-bed Circle Terrace Hospital in Alexandria if it is allowed to open a new facility in Reston.

The state health commissioner has approved both facilities.

When the proposals were considered by the county's Health Advisory Board, both were recommended for rejection because Northern Virginia's hospitals, reflecting a nationwide trend, have been suffering from decreasing occupancy. In the first six months of 1984, the average occupancy rate in the area was about 73 percent.

The board, with Pennino casting the only dissenting vote, agreed yesterday to place the proposed Fair Oaks hospital on the county's master plan, a key step in the county approval process.

The board delayed until Dec. 3 its vote on deciding the requested zoning variance. But Pennino conceded that it was "obvious" the board would approve it.

Mason District Supervisor Thomas M. Davis III was not present for the vote, but has expressed his support.

In other action yesterday, the board voted down a proposal by Supervisor Audrey Moore, a Democrat representing the Annandale District, to impose a 6 percent spending cap on the board's 1986 budget proposals. Board members said they had not yet received enough details on the budget to consider imposing limits.

That action followed Friday's announcement by County Executive J. Hamilton Lambert that school and county officials had agreed on a 4 percent pay raise for county employes next year.