One day after Nassau County District Attorney Kathleen Rice was elected to Congress, candidates have emerged from both parties to run for the office next year, although the immediate decision rests with Gov. Andrew M. Cuomo.

Among the Democrats under consideration, sources said, are former federal prosecutor Joseph Conway, top Rice deputy Madeline Singas, Assemb. Charles Lavine (D-Glen Cove) and former North Hempstead Supervisor Jon Kaiman.

Republican sources said Town of Hempstead Supervisor Kate Murray and Town of Oyster Bay Supervisor John Venditto are eyeing the job.

Rice, a Democrat, will vacate the district attorney's seat on Jan. 3.

Cuomo, a Democrat re-elected Tuesday, can appoint a replacement to temporarily hold the seat or do nothing and allow Singas to take over the office. In either instance, a special election will be held in November 2015. The winner will serve a new four-year term.

A Cuomo spokesman did not respond to a request for comment.

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Rice declined to say whether she had a preferred successor, after initially telling The Associated Press that she favored Singas. "I'm incredibly proud of all we've accomplished in the DA's office, and whomever it is who takes over, I hope it's someone who carries on what we started," she said.

Rice spokesman Eric Phillips said Singas, chief assistant district attorney, "is more than qualified."

"There's a significant advantage to ensuring that a continuity exists capable of continuing the public-safety gains and successful crime-fighting policies of Kathleen Rice," he said.

Phillips said Singas and Lavine, a practicing attorney for more than 30 years before being elected to the Assembly in 2004, are the two most frequently discussed candidates.

Singas declined to comment.

Lavine spokesman Jeff Guillot said the assemblyman, who was re-elected Tuesday, has "interest" in the seat, but is focused on his district.

Kaiman, chairman of the Nassau Interim Finance Authority, said only that the district attorney's job is an "intriguing option."

Conway, a former assistant U.S. attorney who now serves as a defense attorney in Mineola, did not respond to a request for comment.

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Nassau Democratic Party chairman Jay Jacobs will nominate a candidate next spring.A spokeswoman for Venditto declined to comment; a Murray spokesman did not respond to a request for comment.

With Paul LaRocco

and Bridget Murphy