The Prince George's County Board of Education approved a fiscal 1986 budget request of $362.7 million last night, adding about $200,000 to the figure submitted by Superintendent John A. Murphy. County Executive Parris Glendening, however, has already said that lack of funds will force him to cut more than $14 million from the board's request.

The board eliminated funds Murphy had requested for an alternative school for disruptive students. But $243,000 was added to Murphy's request to pay certain teachers to tutor students several hours a week before and after school.

"There is no question this budget . . . is a minimum, modest step forward," said board member Thomas Hendershot, urging the public to lobby state legislators for increased funding for schools.

Board members acknowledged that many of the new expenditures they requested will probably be cut when the County Council sets the final budget figure. Glendening must submit a total county budget by April 1, and the council must finish work on the document by June 1.

Board members, who decided last week to eliminate $182,000 for 10 teachers slated to work in the alternative high school, said they did not disagree with the proposal but wanted more information before setting aside funds. Money for a related proposal by Murphy -- in-school suspension centers -- was retained by the board. And funds for the alternative school may be restored later this year, board members said.

"The feeling was it was just a concept with no clear indication of how it would be implemented," board member Doris Eugene said before the meeting.

Some members expressed concerns about the high school, specifically that it could become populated disproportionately by black students. But Eugene said she believes that if those concerns are answered, "I don't think there's a problem" in approval for the school.

The board also made minor changes in Murphy's budget, adding funds to hire 16 additional special education teachers and 12 full-time librarians.

A move by member Lesley Kreimer to add $22,000 to hire coaches and make swimming an interscholastic sport was defeated.

"It almost seems cruel to put it in knowing full well it will be the first thing to come out," said Eugene.

The board postponed action on a measure that would require parents to inform a school if their child has a contagious disease. But Paul Shelby, who sponsored the measure, said he may withdraw it because existing laws require that such diseases be reported. Shelby and other board members said they want health officials to come up with ways of publicizing those laws before abandoning the proposed measure.

Attention to infectious diseases has cropped up recently in Prince George's and elsewhere across the country, including neighboring Anne Arundel County, where a group of teachers and parents have tried to limit the school attendance of a 3-year-old boy who suffers from herpes. Teachers in a Prince George's special education center also complained about a student who is known to carry cytomegalovirus, an illness resembling flu.

Dr. Robert H. Drachman, director of child health services for the County Health Department, said in a letter to the board that state law requires physicians and health professionals to report "a rather long list of major infectious diseases."

"It appears that procedures which are currently in place are quite adequate to identify those children with significant contagious diseases whose presence might pose a threat to others," wrote Drachman.