The Prince George's County Board of Education somberly approved a fiscal 1986 budget of $349 million last night that leaves intact current programs but provides for substantially fewer improvements than the board had requested.

In cutting $14 million from the $363 million it had originally requested of the County Council, the board eliminated 100 new teaching positions proposed to reduce class size and shelved plans to open discipline centers in the county's high schools.

"The budget we are being forced to adopt is woefully inadequate to upgrade educational programs," said board member Lesley Kreimer. "It does not reflect the vocal support the county government gave to education."

The budget represents a 4.7 percent increase over the 1985 budget of $333.5 million. This year's budget includes $13 million for contracted salary increases. The starting salary of county teachers will increase 5.6 percent in October, rising to $15,738. This year's starting salary is lower than most comparable salaries in area jurisdictions. The starting salary in Montgomery County is $15,561; in the District it is $17,167, and in Fairfax this year was $17,025.

The budget approved last night does not include nearly $5 million that the board requested of the council to finance in part the first year of a magnet school desegregation plan. That request is now before the council.

The $349 million budget represents more than half of the total county budget of $605.1 million approved by the council late in May. The council had reduced the school board's request by $15 million, then later added $1 million.

Superintendent John A. Murphy said he was disappointed with the available funds. "There's so much more that could be done with the resources," he said. "We'll keep going. We're not going to fold up our tents."

Among the few additions to the budget are 12 teaching positions for Project SUCCESS, a program of remedial classes for ninth graders in three high schools. The program will concentrate on improving basic skills, Murphy said, and be available at Suitland, Potomac and Forestville high schools.

Removed from the budget was $227,000 for a new "academic coaching" program proposed by school board Chairman Angelo Castelli. The program would have paid some teachers to tutor students outside school hours.

Among the items requested by the board but eventually eliminated were 14 counselors' positions, 17 secretarial positions, $1.9 million in equipment and $1.2 million in textbooks. The board had requested 12 positions for media specialists but ultimately financed only six positions.

Several board members expressed their frustrations with the lack of funds. "We have the mandate of providing quality education," said Castelli, "but the political fathers refuse to give us the money to do that."