Prince George's County Executive Lawrence Hogan yesterday criticized the county school board for approving a 1981 budget that is 4.1 percent more than this year, and said he thought the board should have agreed to close several county schools.

The school board voted Monday night to send Hogan a $290.3 million budget that cut 532 staff and teaching positions but because of inflation and increased fuel costs, was $11.6 million greater than this year's amount.

Hogan, along with the county council, has final authority over the total dollar amount given each year to run the 127,000-student public school system. He said that because of the county's tax-limiting TRIM amendment, all county departments have been asked to submit 1981 budget requests that are less than this year and he expected the school board to do the same.

"The public schools are losing students every year, so I don't see how they can stay on that constant track of always having a budget go up when enrollment is going down," Hogan said. "They've had increased fuel costs but I think they can be overcome by closing schools."

Hogan said his staff will consider the school board-approved budget and look at possible savings from school closings before making his budget recommendations to the county council next month.

School board members yesterday defended their budget and said that further cuts would do serious damage to the county's educational program.

"I think the executive missed the mark on the size of the budget," said board member Angelo I. Castelli. "You can't look at the school board budget and say it's too high without looking at the services that are to be provided. [Cutting it further] would be a disservice to the county."

School board chairman JoAnn T. Bell also criticized Hogan's statements about school closing and said that while the board realized that some schools eventually will be closed, next year would be too soon.

"We never said we weren't ever going to close schools," Bell said. "We decided to let the issue rest this year because we've been in such an upheavel about closings for the last three years."

Since 1977, the board has voted to close 20 schools, because of declining public school population. In the next three years, the school system is expected to lose another 20,000 students.

The budget approved by the school board Monday is only slightly changed from one proposed by Superintendent Edward J. Feeney last December.

In addition to cutting staff and teaching positions, the board voted to eliminate summer school for elementary students and reduce the amount of money available for new books and other supplies.

Last year, the first under the TRIM mandate, school officials also were forced to adopt a number of controversial cost-cutting measures after Hogan and the council approved a final budget that was $10 million less than the board had requested.

Among the cuts made by the board at that time were reductions in the number of classroom teachers, elimination of junior high school interscholastic sports and the closing of 10 schools.