Boston school officials insist they have looked for money in every corner of their $1 billion budget, but still need to cut services for autistic children, squeeze savings on buses, and delay new programs in order to close the latest shortfall.

But when the School Committee approved the district’s budget Wednesday night, officials did not touch the one area that accounts for the majority of the budget and the greatest rise in spending: teacher salaries, which officials proudly tout as some of the most generous in the country.

As the city enters negotiations for a new teachers’ contract, the district’s perennial budget woes are forcing leaders to consider how they can find firm financial footing without addressing the one item that swallows so much of their budget.

Without a significant increase in state aid, officials warn the Boston schools could face cuts or consolidations for the next several years.

“We celebrate the fact that we pay our teachers more than most of the surrounding areas of Boston,’’ said Eleanor Laurans, the School Department’s budget chief. “But we’re facing a difficult and unsustainable financial trajectory. Something needs to change, otherwise it will become challenging to provide our students the education they deserve, which is our top priority.’’

The average salary for a Boston public school teacher is $90,347. That’s more than in many surrounding communities, including Cambridge ($80,024) and Newton ($75,862) and, when adjusted for local labor costs, more than in 10 comparable districts nationwide, including Cleveland, Denver, and Austin, Texas, according to a city-commissioned study.

Teacher salaries in Boston also start higher and rise faster than in comparable districts in Massachusetts and the student-to-teacher ratio — 12.6 to 1 — is lower than in comparable districts nationwide, according to the study by Education Resource Strategies, a nonprofit consulting firm.

City officials consider the higher salaries and staffing levels an essential ingredient in the effort to improve schools.

“In order to attract the top-quality talent, as far as teachers, we have to pay them well,’’ Mayor Martin J. Walsh said.

But the costs are squeezing district finances.

A more than 20 percent rise in school spending over the past five years — from $815 million to more than $1 billion — has been driven largely by growing salaries and benefits, which constitute 71 percent of the increases, according to the Boston Municipal Research Bureau. As with most city departments, employees — not buildings or services — are the biggest expense.

School officials also blame the State House for their annual budget deficits.

State education aid to Boston has dropped by $6 million during the last five years. State lawmakers have also failed to fully reimburse Boston for the state aid it loses to charter schools, costing the city $11.6 million this year, according to the research bureau.

“Those are the things that hurt us,’’ Walsh said.

The mayor said it may be years before Boston can balance its school budget without cuts.

“For the next couple of years, we’re going to have difficult budgets until we right-size everything,’’ he said.

One idea under consideration involves closing schools, which would almost inevitably trigger layoffs.

A city-commissioned study by McKinsey & Co. found that even though enrollment has plunged over four decades to 57,000, Boston still maintains seats for 93,000 students spread across 126 schools, forcing the city to pay for more school buildings than necessary.

Samuel R. Tyler, president of the research bureau, said there is no need for Boston to maintain such a large and costly system.

“The decision is made for this school year coming up that there will be no school closings,’’ he said. “This is the last year that can happen. Otherwise, we’re going to continue to be in the same situation — not having enough resources.’’

Closings would undoubtedly spark protests from teachers, parents, and students, particularly if schools are shuttered just as the state lifts the cap on the number of charter schools allowed in Boston and other communities.

But city officials argue the savings could prevent more painful cuts to classrooms.

“At the end of the day, we’re not making a cut, per se,’’ Walsh said. “We’re trying to realign the money and reinvest the money into kids’ education.’’

With the teachers’ contract set to expire in August, union officials could also face pressure to limit future pay increases. The last contract, approved in 2012, granted teachers a 12.6 percent salary increase over six years.

City officials may also seek concessions such as a longer school day. Last year, the teachers’ union agreed to add 40 minutes to the school day in 60 schools. But Boston still has one of the shortest days of any urban district.

“With the added benefits and salary — which I don’t begrudge — there needs to be some consideration given toward the length of the workday,’’ said Michael Contompasis, a former Boston schools superintendent.

City officials also complain that they have to pay $13 million in salaries and benefits for about 100 teachers who were not assigned to classrooms this year. Many returned from leaves of absence and were unable to find jobs, or were ousted from underperforming schools, which are given more flexibility to dismiss staff.

“Without a change in state law, this subset of teachers will remain in our system for years, diverting resources away from needed investments,’’ Walsh told the Legislature earlier this month. “We simply ask for the flexibility to address this challenge.’’

Richard Stutman, president of the Boston Teachers Union, said that rather than fire those teachers or close schools, city officials should oppose efforts to lift the charter school cap and push for additional state aid and for larger payments from universities, hospitals, and other large nonprofits, which do not pay taxes.

“Every year, we go through the same tug-of-war,’’ Stutman said. “The city has got to do a better job of bringing in resources.’’

City Councilor Tito Jackson said schools should be protected from cuts next year, when the city is projected to collect $95 million in additional property tax revenue.

“Why is that money not being used to invest in our public school system?’’ Jackson said.

Tyler said the $95 million will be used to fund schools but must also cover the rising cost of debt payments, pensions, and salaries and benefits for other city workers. He pointed out that, over the last five years, Boston has boosted school spending by more than 20 percent, compared to 13 percent for other departments.

“It’s not as if the city hasn’t been supportive of public education,’’ Tyler said. “But you can’t keep putting more money into the system if they’re not going to become any more efficient.’’

Michael Levenson can be reached at mlevenson@globe.com. Follow him on Twitter @mlevenson.