Tax rebate checks are beginning to be received by Long Island homeowners and many of them are substantially larger than last year.

However, some checks have been reduced because local governments failed to meet state requirements for the rebates.

About 600,000 checks will be sent to Nassau and Suffolk counties under the state Property Tax Freeze Credit program between now and early next year, said Geoffrey Gloak, a spokesman for the state Department of Taxation and Finance. A similar number were delivered between late 2014 and February.

He said the department doesn’t yet know the average size of the checks bound for Long Island. It was $173 last year.

The rebate offsets “two years of school tax increases and one year of increases for all other [taxing] jurisdictions, as long as they complied with the requirements,” Gloak said. “We expect that, statewide, the average credit amount will be 2.5 times more than last year.”

Besides school districts, the rebate program now includes other local governments that levy property taxes, including counties, towns, cities, villages and special districts for libraries, fire protection, garbage collection and other services.

The state sets requirements for each jurisdiction’s taxpayers to be eligible for the rebate program, which was adopted by Gov. Andrew M. Cuomo and the State Legislature as part of the 2014-15 state budget.

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To receive a rebate of a school tax increase, the school district cannot have pierced the state-imposed 1.56 percent tax cap this year.

The district also must have a cost-savings plan, called a “government efficiency plan,” approved by the state Division of Budget. On the Island, schools account for about 70 percent of the typical property tax bill.

State officials said this week that residents of the East Meadow, New Suffolk and Quogue school districts wouldn’t receive a rebate of their 2015-16 school tax increase. East Meadow’s hike exceeded the tax cap, and New Suffolk, Quogue and East Meadow don’t have approved plans, said Morris Peters, a budget division spokesman.

Two local towns — Oyster Bay and Shelter Island — and 20 villages adopted tax increases that are higher than the tax cap, according to data from the state comptroller’s office. So their residents aren’t eligible for a rebate of those tax hikes.

The affected villages are Belle Terre, Brookville, Cove Neck, Dering Harbor, Great Neck, Great Neck Estates, Head of the Harbor, Hempstead, Hewlett Neck, Kings Point, Lynbrook, Malverne, Munsey Park, North Hills, Ocean Beach, Old Westbury, Patchogue, South Floral Park, Upper Brookville and Williston Park.

Rebate checks are being mailed once a county’s tax rolls are sent to Albany. Most of Nassau’s rolls are in, while Suffolk’s haven’t yet been received, according to Gloak.

To be eligible for a tax rebate, homeowners must qualify for a separate program — the STAR property-tax exemption — and live outside New York City. Their 2013 household income must have been $500,000 or less. The rebate is only on the taxpayer’s primary residence, not a vacation place or second home.

More information is available at on.ny.gov/1OOQg6r or by calling the Tax Department at 518-453-8146.