The Prince George's County Council approved the county executive's $670 million spending plan for fiscal 1987 nearly intact yesterday. It includes a $40 million increase for the school system and will allow the hiring of 65 police officers and 20 firefighters.

The budget for the year beginning July 1 is about 10 percent bigger than last year's, but will be covered by an expected $30 million increase in taxes and other revenues from house sales and construction, county officials said. The property tax rate in Prince George's will remain at $2.40 per $100 of assessed value, although homeowners' taxes will rise as property assessments increase.

The council added $1.04 million to the budget proposed by County Executive Parris Glendening in April, with the largest share, $905,449, going to the county's professional and volunteer fire departments.

Of that amount, $505,449 will permit the hiring of 10 full-time firefighters and the purchase of a mobile intensive care unit to serve the southern part of the county. Volunteer fire companies will receive $400,000 for new equipment.

Included is the $389 million for county schools requested by the Board of Education and proposed by Glendening.

The additional $40 million is to be used to expand the magnet schools program, boost annual salaries for first-year teachers from $15,700 to $19,000, buy additional textbooks and supplies, and decrease class sizes.

By shifting funds within the Board of Education's budget, the council added $200,000 to increase the number of reading teachers at elementary schools, $100,000 to buy textbooks and $200,000 to fund a summer school program for students who do not attend "compensatory education" schools. The additions were offset by a reduction in the school system's contributions to the worker's compensation fund.

Generally, the council made few changes in the county executive's budget proposal.

School spokesman Brian J. Porter said the school board is "deeply pleased by the level of commitment shown by the county government" to improve the quality of the school system.

"It sends a signal throughout the county school system that work under way is being supported," he said. "That has a tremendous morale factor. It has a ripple effect that goes beyond dollars and cents."

Among the changes the council made in Glendening's budget proposal were the addition of $75,000 for the Department of Aging to buy new buses to transport senior citizens, $80,000 for a county program of loans and grants to provide indoor plumbing for about six low-income families in rural communities in southern Prince George's, $50,000 to improve services for homeless people in the county, and $56,000 for the Department of Environmental Services to make background checks on day care workers.

Glendening, who applauded the council's work, is expected to sign the budget next week