Long Island’s public schools gain an extra $155 million in state operating aid for the next academic year — including more than $90 million owed from the past — under the budget agreement reached by Gov. Andrew M. Cuomo and lawmakers.

The 6.16 percent hike in state financial assistance to districts in Nassau and Suffolk counties will bring the region’s total aid in the 2016-17 school year to $2.97 billion — a record. The additional aid is nearly $50 million more than the amount the governor proposed in January.

State aid from Albany makes up about 25 percent of districts’ revenues on the Island, with local property taxes providing most of the remainder. The state’s caps on property taxes are particularly tight this year, making districts more dependent than ever on the assistance.

“We have provided record aid to education, especially since we regained our majority,” said Senate Majority Leader John Flanagan (R-East Northport). “Everything we do keeps the local property levy down.”

Flanagan was referring to the effect of statewide elections in 2010, when Republicans led by the Island’s delegation retook control of the chamber after several Democratic senators lost their seats.

Local educational leaders were restrained in their response Friday. The statewide aid increase of $1.35 billion was the highest since the 2008-09 school year, but fell short of the $1.7 billion that educators had said they need to keep classroom programs running at current levels.

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“We’re always grateful for the money that comes,” said Julie Lutz, chief operating officer of Eastern Suffolk BOCES and a leading analyst of fiscal trends. “But in a year when we’re faced with a .12 percent tax-levy limit, it’s not going to be sufficient. I think it’s going to mean cuts.”

“It’s in the right direction,” said Nathan Jackson, a spokesman for Wyandanch schools, which won a $1.4 million aid increase. “But we’re gaining five new students on an average day, and just to expand classrooms will cost more than a million dollars.”

One special feature of the new aid package is that it restores — for the coming year, at least — aid that Albany cut from districts’ revenues in 2010-11 and 2011-12. Those reductions, pushed by Cuomo and his predecessor, Gov. David A. Paterson, were made to cope with a state budget crunch stemming from the nationwide recession.

Restoration of the money, known as the Gap Elimination Adjustment, or GEA, was a high priority on the Island. Many school districts in the region, because of their relatively high wealth, suffered heavy losses of GEA money, and the state’s repayment will eliminate a source of fiscal annoyance.

The Three Village district got an aid increase of $2.44 million, or 8.16 percent; Half Hollow Hills got $2.47 million, or 9.97 percent; and Sachem received $8.23 million, or 8.1 percent.

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Sachem, the Island’s second-largest district, had announced before last week’s aid agreement that its proposed spending plan probably would exceed its state-imposed tax cap. Such action requires approval by a 60 percent “super majority” of those voting on the district budget in mid-May.

On Friday, Sachem’s associate superintendent for business, Bruce Singer, said he would discuss the aid increase with the district’s school board at its next meeting on April 13. Singer would not say if he might recommend staying within the district’s cap limit, but noted, “Obviously, we are in a different financial situation now that the state has restored the GEA.”

In Amagansett, another district considering a cap override, Superintendent Eleanor Tritt said work on the budget had not been completed, but that the district still expected to seek 60 percent voter approval of a cap override.

Amagansett, a tiny East End district, will get an aid hike of $8,412, or 2.52 percent, in the next school year.

One wrinkle in the GEA restoration is that not all of the repaid money is included in districts’ regular aid allotments. Instead, about $25 million in restorations Islandwide are listed as separate payments.

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Some local school administrators voiced concerns Friday that the separate GEA payments might be for one year only and the funds will not be built into their aid formula going forward.

“Therefore, we are going to see our state aid in the future permanently reduced by $196,000,” said Joseph Dragone, assistant superintendent for business in Roslyn, citing his district’s GEA figure.

However, Robert Lowry, deputy director of the New York State Council of School Superintendents, said state law clearly eliminated the GEA permanently, and others agreed.

“It’s not G-E-A, it’s G-O-N-E,” said Flanagan, spelling out the letters.

With Michael R. Ebert and Candice Ferrette