Fewer opportunities for employment in metropolitan Washington will be available during the next three months, a recent survey of private and public employers shows.

The employment outlook survey, conducted quarterly as part of a national poll, found that only 17 percent of the area's employers plan to increase their work forces during the first quarter of 1982; 28 percent said they expect to reduce their staffs.

Survey results were released today by Milwaukee-based Manpower, Inc., a temporary employment service firm and a subsidiary of Parker Pen Co. The survey is based on interviews with more than 10,000 employers in more than 300 cities.

Nationally, employers forecast a sharp drop in hiring activity, indicating the worst quarter in the six years that the poll has been conducted.

In the District, 43 percent of those surveyed said they plan cutbacks, while only 28 percent indicated they plan to add to their staffs.

Only 3 percent of employers in Northern Virginia plan to hire more workers, while 33 percent will initiate cutbacks. Suburban Maryland employers provided a more optimistic outlook. About 15 percent said they expect to add to their staffs and only 20 percent plan reductions.

In another development, Bethlehem Steel, Maryland's largest private employer, began layoffs of 6,100 workers yesterday at its Sparrows Point plant for at least one of two weeks.

A company spokesman said the reduction was caused by the sagging demand for domestic steel, the need to shut down mills for repairs, and vacations. The layoffs will be without pay.