Veteran Suffolk Legis. Jay Schneiderman said he has turned down an offer by East Hampton Republicans to run for town supervisor and will seek re-election as a county lawmaker this fall.

If re-elected, Schneiderman's new term will be his last under the county term limit law.

"There still a lot of work to be done at the county," Schneiderman (I-Montauk) said in a statement Monday. He noted issues including the county's fiscal problems, the economic struggles of low-income South Fork residents and beach erosion in Montauk following recent storms.

Schneiderman, 50, who is in his 10th year in the legislature, said Democratic County Executive Steve Bellone and county Democratic chairman Richard Schaffer asked him to remain in the legislature. However, Schneiderman did not foreclose the possibility of a future run for town supervisor.

Schneiderman, a former Democrat who served previously as supervisor as a Republican, had screened for the top town job with the town Republican and Democratic parties, seeking both endorsements. But Democrats appear poised to name Larry Cantwell, 62, who is retiring as East Hampton Village administrator, as their candidate.

The local GOP backed Schneiderman after two-term Republican incumbent William Wilkinson declined to screen. Wilkinson said he will not run again.

"I'm a little disappointed," said Kurt Kappel, East Hampton GOP chairman, while noting that Schneiderman made his decision early enough to give the party ample time to find another contender.

"Jay wanted a coronation and didn't get it," said Wilkinson, referring to Schneiderman's bid for cross-endorsements by both major parties. "The East Hampton Republicans did a terrible job of strategizing," hurting any new candidate it chooses, Wilkinson said. "It's like being second choice for the prom."

John Jay LaValle, Suffolk Republican chairman, said term-limited Southampton Town board member Christopher Nuzzi, of Westhampton, is interested in challenging Schneiderman for the legislative seat. LaValle said Schneiderman is vulnerable because he has "carried Bellone's water" on budget issues and "bounced around from party to party."

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But Jon Schneider, deputy county executive, called Schneiderman a "strong voice" for the East End who is influential on county fiscal issues.