A private company that has provided medical care to Nassau County inmates since 2011 on Monday sued the county to cease services at the end of May when its contract ends.

In the lawsuit, Armor Correctional Health Services of New York Inc., based in Florida, said it notified Nassau County Executive Edward Mangano’s administration many months ago of its intention to pack up its operation on May 31 when its contract with the county expires. The company said it reiterated its position again last month and urged county officials to expedite selecting a new provider because it could take up to 60 days to train new workers.

“Any request by the County that Armor continue providing services for an indefinite period of time beyond the expiration of the Contract and without the renegotiation of key Contract terms including those affecting Armor’s compensation, is not reasonable,” the company said in the lawsuit filed in State Supreme Court in Mineola.

Armor — a for-profit company that provided health care services to Nassau inmates since June 2011 — has come under fire after several inmate deaths at the facility in East Meadow.

While Armor wants to end its relationship with Nassau no later than May 31, Carnell Foskey, the Nassau County attorney, said a clause in its contract requires Armor to stay on until the county hires a new vendor to take over, and help with the transition.

“The County disagrees with Armor’s interpretation of the contract and will vigorously defend the lawsuit,” he said in an email.

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Armor said if the court requires it to continue providing health care services to the more than 1,000 inmates at the Nassau jail, the company asked that it be contingent on Nassau County having a new operator take over on June 1.

The Mangano administration was negotiating with another for-profit company, Correct Care Solutions, based in Tennessee, to take over for Armor. But talks broke down with Correct Care Solutions broke town last month, forcing the administration to start the search over.

Bidders interested in the multimillion-dollar contract have until April 6 to submit their applications.

Minority Leader Kevan Abrahams (D-Freeport) said two months is not enough time for the county to select a new vendor, negotiate a new contract, and present it to the Nassau County Legislature for approval.

“I don’t see this happening until the middle of the summer,” Abrahams said Monday. “I would love to be wrong because that means we’ll get Armor out quicker. But realistically, I don’t see it.”

To complicate matters, Armor, which provides health care services to more than 40,000 inmates in eight states, settled a lawsuit brought by the New York State Attorney General Eric T. Schneiderman, alleging inadequate care. As part of the settlement, Armor agreed not to “enter into any contract” with any local government in New York for three years starting in October 2016.

The attorney general “has expressed the view that Armor should not provide healthcare services to inmates at NCC beyond May 31,” according to the lawsuit.

Armor asked the court to declare that the company would be in breach of its agreement with the attorney general’s office if it remains on after May 31. Extending its services, even on a month-to-month basis, would require Armor to sign a new contract with Nassau.

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A spokesman for Schneiderman on Monday declined to comment.