One-third of $117 million in state financial aid owed to Long Island’s public schools would be repaid next year under Gov. Andrew M. Cuomo’s budget blueprint — a proposal that displeased local education leaders expecting to face the tightest tax cap ever this spring.

The owed money, known as the Gap Elimination Adjustment, or GEA, represents the balance of state funding cut from school districts’ revenues in 2009-10 and 2010-11 at the height of a fiscal crisis and never returned. Every year since, each system’s outlay has carried forward on state-aid breakdowns as “GEA Restoration.”

Cuomo, in his annual budget message Wednesday, called for repaying $434 million in statewide GEA obligations over the next two years. His plan is a departure from recommendations by major education lobbies and the policymaking Board of Regents, all urging complete repayment during the 2016-17 school year.

Under the governor’s spending plan, the money also would not be repaid to districts in equal annual installments.

Schools in Nassau County would get back $14.9 million of nearly $45.2 million owed by the state in the next school year, according to district-by-district figures released by the governor’s Division of the Budget. Suffolk schools would get $24.3 million next year of $72.4 million owed.

Individual districts that would be left, in effect, with large state IOUs at the end of the next school year include Sachem, with $6.2 million in projected state obligations; Longwood, $2.7 million; Patchogue-Medford, $2.5 million; and Three Village, $2.3 million.

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“We’re disappointed,” said Julie Davis Lutz, chief operating officer of Eastern Suffolk BOCES and a leading regional financial analyst. “It’s been a long time.”

Local experts contended that school-aid cuts imposed in the past by Cuomo and his predecessor, Gov. David A. Paterson, have had a strong cumulative effect as the years rolled by, the state enacted its property-tax cap, and districts had to reduce staffing and student services.

“We’ve lost over $1.2 billion, so elimination of the GEA is only fair,” said Joseph Dragone, assistant superintendent for business in the Roslyn district, referring to the combined loss of Long Island’s 124 districts over time.

Further, school systems are braced for news from the state comptroller’s office this month on tax-cap limits. The low inflation rate is expected to force districts to hold proposed 2016-17 budgets to near-zero tax increases, even as salaries and other education costs are rising.

Other aspects of Cuomo’s budget, which would raise statewide school assistance by $2.1 billion over the next two years, get higher marks from many authorities.

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Senate Majority Leader John Flanagan (R-East Northport) called the governor’s plan “an excellent start,” though he also has vowed to increase the package and pledged to local districts that the GEA would be entirely erased in 2016-17.

State operating aid for Nassau and Suffolk schools would rise $105.7 million next year under Cuomo’s proposal, to a total $2.6 billion. That figure does not include assistance for school construction and renovation, which is reimbursed to districts where voters approve such projects.

Morris Peters, a spokesman for the governor’s Division of the Budget, said the state’s overall aid payments to Long Island’s schools in 2016-17 would total $3 billion — up 4.5 percent from the current year and at a rate higher than the state average.

“The governor’s budget reflects his strong commitment to education,” Peters added. He did not address the GEA issue directly when asked.

The 500-page book released by Cuomo’s office explaining his budget said spreading the GEA repayment over two years “allows school districts a predictable revenue stream to enhance long-term financial planning and support responsible budget practices.”

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Some veteran educators observed that the state’s legislative season appears to be unfolding in the usual way, with a governor proposing relatively modest aid increases and lawmakers vowing to up the ante.

Both the Regents and the state’s Educational Conference Board, representing teacher unions and other major school groups, have recommended aid increases of more than $2 billion next year, compared with Cuomo’s proposal of nearly $1 billion. Many analysts expect the ultimate package to come out closer to the former figure, especially in a state election year.

GEA reimbursement is an emotional issue that has left school systems across the state sharply split.

On the Island, most school boards and superintendents since 2013 have listed restoration as their No. 1 priority. Those leaders noted that their schools in 2009-10 and 2010-11 suffered larger aid cuts on average than the state as a whole, because of the region’s slightly higher wealth.

In contrast, New York City and other urban school systems have argued for bigger increases in state “foundation” aid, which is distributed by a formula that gives greater weight to districts with concentrations of impoverished students. Some districts on the Island, such as Brentwood and Central Islip, also benefit from such assistance.

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That point was underlined on Sunday, when advocates of the foundation-aid approach rallied on the steps of City Hall in Manhattan. Some of those advocates, who won a state court ruling in 2006 driving more money to their schools, suggested that focusing on GEA restoration would widen the inequality gap between affluent and less-affluent districts.

Many of the Island’s educators rejected the implication that their districts, which pay high school taxes, could be considered privileged.

“Longwood is a working-class community that strongly supports the education of its children,” said Dan Tomaszewski, the board president there. “It certainly deserves a fair share of funding from the state of New York.”

Financial pressure is ramped up this year because of the state’s tax-cap restriction on school budget increases: The cap is either 2 percent or the inflation rate, whichever is lower, and the inflation rate has remained unusually low.

Local school administrators said a limit that tight will leave their districts virtually dependent on Albany for money needed to meet ordinary expenses without cutting student programs. The Educational Conference Board estimates that schools statewide next year will need about $1.7 billion, or a 2.7 percent increase, to maintain existing programs. Costs are driven primarily by salary hikes.

Thus, school officials said, the aid increase offered by the governor is unlikely to meet their needs.

But not everyone accepts that argument.

Cuomo, for example, noted in his budget message that New York State already spends an average $19,818 per student — the highest cost among all states. Figures are based on U.S. Census Bureau calculations for 2013.

Meanwhile, New York’s student achievement falls in the middle of the pack, according to recent federal testing of student sample groups in each state.

A conservative analyst, Timothy Hoefer, said the argument by school groups that they need an additional $2 billion-plus in aid “doesn’t hold water when studies show we’re not getting the best schools.” Hoefer is executive director of the Empire Center for Public Policy, an Albany-based think tank.

Another hot issue is proposed help for nonpublic schools. Cuomo has proposed $150 million in education tax credits for private donors who contribute either to scholarship organizations or public schools. Advocates said this would be of particular help to private and parochial schools in urban areas, many of which have waiting lists of applicants.

But representatives of public schools, such as Michael Borges, executive director of the New York State Association of School Business Officials, said the state should not be “diverting” funds to nonpublic schools at a time when it still owes GEA money to the public sector.

“It’s like buying a new house when you still hold a mortgage on your old house,” Borges said.