At least 768 more Long Island homeowners have completed all paperwork and repairs through the NY Rising program and have either received or are on track to get a final check from the state, according to a quarterly report.

The additional homeowners — 613 in Nassau and 155 in Suffolk — finishing the process of receiving compensation for damage from superstorm Sandy, marking a 40 percent increase in closed cases since the previous report. In Nassau 1,978 cases were completed by the end of May and 714 cases were finished in Suffolk, according to the report on single-family housing from March through May.

In addition, since the report was released last month, another 428 homeowners on Long Island have closed out their cases, said Barbara Brancaccio, a NY Rising spokeswoman.

“The Governor’s Office of Storm Recovery [which manages the program] has made extraordinary progress disbursing hundreds of millions of dollars to Long Island homeowners, leading the region in Sandy recovery,” Brancaccio said.

State officials have said superstorm Sandy, which struck Oct. 29, 2012, damaged 95,534 Long Island structures, including more than 50,000 single-family houses.

Homeowners turned to several programs after the maelstrom to help rebuild, including NY Rising’s Housing Recovery Program.

To date, 10,861 single-family homes on Long Island have signed up for that program and have received either full or partial payments for repairs. Statewide, 11,722 homes have participated in the program.

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Closed-out cases now represent 25 percent of all homeowners who have received NY Rising payments, up from 18 percent of recipients since the last report.

The remaining 8,169 Nassau and Suffolk cases consist of homes that have received partial payments amounting to between 50 percent and 75 percent of their awards, a drop of 638 or 7.2 percent from the previous report’s figure of 8,807.

State Sen. Todd Kaminsky (D-Long Beach), who drafted the legislation as an assemblyman along with state Sen. Tom Croci (R-Sayville) that requires the state Governor’s Office for Storm Recovery to compile the numbers in a more easily readable format, said the pace needs to pick up.

“Since the last report, another 613 families have been closed out of the NY Rising program — at this pace it will be another 2 1⁄2 years before every Sandy victim is fully paid,” he said in a statement, referring to Nassau’s caseload at the time the report was released. “While progress has been made, I urge NY Rising to redouble its efforts and am prepared to work with anyone involved to ensure that Sandy victims return home as soon as possible.”

State officials said they have now distributed over $493 million in Nassau and $208 million in Suffolk. At the time the last report was released, the state had distributed $459 million in Nassau and almost $193 million in Suffolk.

New York State manages about $4.4 billion from the federal Department of Housing and Urban Development to fund a number of programs designed to help homeowners, municipalities and businesses recover from Sandy and tropical storms Irene and Lee.

Those include the repair program as well as a “buyouts and acquisitions” program through which the state has purchased damaged homes and resold some of them back to the public, a mortgage assistance program, and funding to elevate homes.

The single-family homes report also showed that 130 more Long Island homeowners were added between March and May to the group that received partial or full payment, a hike of 1.2 percent from 10,731 to 10,861, with 8,056 in Nassau and 2,805 in Suffolk.