Montgomery County School Superintendent Harry Pitt yesterday proposed a $576 million operating budget for next year, a 10.6 percent increase that he said is necessary to meet soaring enrollments, open seven new schools and pay negotiated teacher raises.

At the same time, Pitt's first budget since becoming superintendent in July contains few improvements to the school system, an apparent attempt to mend frayed relations with the County Council, which made unprecedented cuts in the school budget request last year.

Most of the proposed $55.1 million increase to the school system's current budget would pay for previous commitments: opening six elementary schools and a high school, fulfilling the terms of three-year labor contracts by giving 8 percent annual raises to teachers and 5 percent to service workers, and educating an anticipated 2,800 more students -- the biggest enrollment spurt in two decades.

Pitt has devoted $3.8 million -- less than 1 percent of his proposed budget -- to improvements and additions to current school services. They include a slight reduction in elementary class size, more elementary guidance counselors and school psychologists, and the beginnings of a campaign to improve the recruiting and retention of teachers.

"All of these improvements focus on the classroom and the school," he said, attempting to rebut past criticism from county officials that the school system is top-heavy with administrators.

Pitt followed the custom of his predecessors, repeatedly emphasizing what he called the conservatism of his request. "This is an extremely modest, conservative budget," he said at a morning news conference.

Uncustomarily, County Council members agreed. "I think this is a very temperate and reasonable request," said council President Michael L. Subin.

Subin and council member Isiah Leggett -- two of the three Education Committee members -- predicted that Pitt's proposal will ward off a repeat of the unusually fractious debate over the school budget last year. That debate ended with the council cutting $20 million from the school board's request, including an unprecedented $8 million in existing services.

"This year we're starting off much closer," said Leggett.

"The environment a year ago was probably close to 180 degrees different than it is now," Subin said.

In fact, the main opposition to Pitt's proposal yesterday came from those who suggested that the superintendent is being too conciliatory.

"It is a very austere budget," said Mark Simon, president of the Montgomery County Education Association, the school system's main teacher union. "His justification is, when the county is just keeping up with an influx of students, we can't also make improvements. I can't buy that. I don't think the citizens buy that."

The release of Pitt's proposal marked the opening day of a budget season that will conclude in May, when the County Council adopts a budget for fiscal 1989. The school board is scheduled to hold public hearings Jan. 19-21 and to vote on a recommended budget Feb. 9. The board will submit its recommendation to County Executive Sidney Kramer, who will make his budget recommendation to the council.

Yesterday, Kramer said he had not reviewed Pitt's proposal and could not comment on it.

Pitt said the school system will need 152 new elementary and high school teachers, at a cost of $4.2 million, to cope with expanded enrollment, primarily from a development boom in the northern and western parts of the county.

In addition, he said, the seven new schools -- the largest number opened in a year since 1968 -- will require 104 positions, at a cost of $4.7 million. There will be start-up costs of $3.2 million for such things as textbooks, library materials and equipment.

School board and County Council members had little disagreement yesterday with Pitt's calculation that the schools will need a $51.3 million increase just to maintain basic services. "I don't know how that can be changed," said Sharon DiFonzo, the school board president. "It is the high cost of standing still."

Also, Pitt recommended that the county, for the first time, phase in a series of improvements over four years.

"I want to set some goals we can more toward," he said, adding that he did not believe that the county can afford them all at once. In all, they would cost $11.7 million, Pitt's figures showed, although he is seeking only $3.8 million for next year. His predecessor, William Cody, sought $8 million in improvements last year.

Included in Pitt's suggested improvements are restoration of summer school programs and after-school bus service, which were victims of last year's budget cuts. Most school board members said yesterday they planned to tinker with his proposal but were essentially satisfied with it.

Commented school board member James Cronin. "I'll make do with less at this point. I won't make it a knock-down, drag-out fight." But board member Blair Ewing said he wants to add $2 million to $3 million in improvements to accomplish several goals more quickly. HIGHLIGHTS OF PROPOSAL

$576 million budget -- 10.6 percent more than this year.

$28.2 million -- or 51.2 percent of total increase -- to cover negotiated salary increases.

$9.8 million to cover expenses of increased enrollment, seven new schools.