Montgomery County Executive Charles W. Gilchrist yesterday proposed a $353 million county school system budget that puts him at odds with school board officials who argue it would adversely affect the quality of education they can deliver.

The board has submitted a budget request for $356.6 million that it said contained no fat at all, but Gilchrist, sticking with a stance he originally took March 1, said his recommended budget recommendation represented a 5.7 percent increase over the previous year and would permit "substantial enhancement throughout the system.

"The growth recommended by the board . . . is disproportionate when viewed in the context of declining enrollments and does not offer assurances to the public that every effort has been made to achieve efficiencies," Gilchrist said in a memorandum to County Council President Neal Potter. The council must approve the school budget.

School board members countered that the public is more concerned with the quality of education than fiscal conservatism. Suzanne Peyser, the school board's vice president, said, "The executive has made some cuts in some areas that will really hurt instruction."

When Gilchrist first made his budget recommendations in March, school board members said they feared there would not be enough money to meet a major goal, moving from a six-period to a seven-period school day in high school. Yesterday Gilchrist said his budget would provide $986,792 for that purpose and added that other improvements would include more kindergarten and reading teachers, as well as instruction in word processing and computers.

One of Gilchrist's main arguments against the board's proposed budget increase was what he called a major rise in per-pupil expenditures over the past several years even as enrollment in the county school system was falling from more than 126,000 in 1973 to about 95,000 now.

Board member Eleanor Zappone assailed that argument as "deceiving and misleading." Zappone said that budget increases had been eaten away by rampant inflation and special instruction requirements like the $10,000 to $20,000 per year it costs to educate a handicapped student.

Although the school system's budget director, Ken Hill, acknowledged that Gilchrist's budget outlay was only 1 percent below the board's request, he outlined several areas where planned improvements were cut.

Hill said the school system wanted 10 more kindergarten instructors; Gilchrist recommended three. The board wanted 40.5 new positions in elementary schools to cut class size, but Gilchrist asks no change.

Gilchrist also recommended $200,000 less for utilities than the school system wanted. "This isn't a forecast of doom," he said, "but if there is a harsh winter . . . ."