The Prince George's County Board of Education last night approved a $290.3 million budget proposal that has been criticized as too austere yet calls for $16 million additional aid from the county government.

The proposed spending program is nearly $10 million above what County Executive Lawrence J. Hogan has said the county can afford. It sets the stage for a major confrontation over revenues, which are already severely limited by the county's tax-limiting TRIM charter amendment that voters approved in 1978.

The school board made few changes in Superintendent Edward J. Feeney's $290.1 million budget proposal, which drew strong criticism at public hearings from parents and the 20,000-member County Council of PTAs as being too austere.

The budget now goes to Hogan and the County Council.

It calls for eliminating 532 teaching and staff positions, discontinuing summer school for elementary pupils and cutting 37 percent from the current expenditure for replacing equipment.

School officials say the personnel reductions, to be accomplished through attrition, would not affect class size becase enrollment is declining.

At one point in last night's discussion, board member A. James Golato said, "We have to remember that what we do . . . probably won't stick. What we need to show the people across the way [Hogan and the council] is that we acted in good faith and accepted the superintendent's bare-bones budget. If we do anything else, we may be just asking for unneeded confrontation. We don't need to come up with a Christmas tree of add-ons."

Countering Golato, board member Norman Saunders, sponsor of several amendments to add to the budget, said, "with inflation running at such a high rate, this is not just a bare-bones budget. This is a budget that cuts right into the marrow of the bone." Saunders' amendments were defeated.

The $209.3 million budget request is only 4.1 percent above the current fiscal year's budget. Much of the increase is the result of inflation, rising fuel costs and teacher raises.