The Montgomery County Council approved a $782 million operating budget early yesterday, but after 14 hours of debate, appeared to leave unresolved the urgent issue of how the county will solve its controversial solid waste disposal problem.

In adopting the new budget, the council approved funds for operating a waste disposal landfill for the year that begins in July. However, before moving to the new budget, the council failed, after arduous efforts to reach a compromise, to appropriate $600,000 needed to open and operate the controversial new Oaks Landfill in Laytonsville next month.

A proposed restriction that would have specifically prevented the money in the new budget from being used to operate the Laytonsville landfill was rejected by the council. Therefore, said council member David Scull, "The result of the budget vote is that the landfill can open."

But Council President Neal Potter said in an interview that he considers the situation unresolved. With the county's authority to operate its present dump expiring May 31, Potter explained, some waste disposal plan must still be made for June. He said he expects that whatever plan is implemented may remain in effect until the controversy over the Laytonsville site is settled.

Disputes have arisen over possible pollution hazards at the Laytonsville dump, and neighbors have filed lawsuits to block its opening. In a new development yesterday, County Executive Charles W. Gilchrist agreed to meet with the Environmental Protection Agency to discuss the safety of the dump.

The budget, approved by the seven-member council shortly after midnight, lowers the county's tax rate by 3 cents, to $3.23 per $100 of assessed value, according to Potter. A significant rise in assessments, however, will result in an increase in tax bills. The bill for the owner of a $100,000 house that was reassessed last year, for example, will increase from $1,552 to $1,607, based on the county's triennial assessment plan.

A "no frills" budget of $781 million was proposed last March by Gilchrist, who later added $330,000 to improve the academic program at Montgomery Blair High School and another $166,000 for health benefits for retired teachers.

The all-Democratic council went along with those additions, but then cut the budget by $400,000. In the largest single area of the budget--the county's public schools--education officials had asked the council to increase the $353.4 million proposed by Gilchrist.

Instead, the council shaved $311,000 from Gilchrist's proposal, which public school officials said will blunt their efforts to improve educational standards.

"We wanted 40.5 teacher positions at the elementary level to decrease class size and didn't get that," said Superintendent Edward Andrews. He said the schools only received 18 new full-time positions.

Potter defended the budget as a fiscally responsible one, and one that does not decrease county services.

"Most of the so-called 'fat' was pared from the county budget in previous years, and it has taken some ingenuity to . . . arrive at this fiscally prudent budget which preserves most of the high quality services . . . the citizens of Montgomery County have come to expect."