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The second-largest union of New York State employees has rejected a package of wage and benefits concessions negotiated by Gov. Andrew M. Cuomo, dealing a jarring setback to the governor that is likely to prompt several thousand layoffs.

The union, the Public Employees Federation, which represents 56,000 state workers, announced on Tuesday that its members had voted 54 percent to 46 percent against the contract, which would have imposed a three-year freeze on wages and increased health insurance costs. The vote took place by mail over several weeks.

The president of the union, Kenneth Brynien, said that members were ready to make sacrifices given the state’s shaky fiscal condition but that they felt the concessions Mr. Cuomo insisted on were beyond what was reasonable.

“The cuts that are demanded of them in this tentative agreement were just too many, and they cut too deep,” Mr. Brynien said at a news conference. “The sacrifices were too great, and they said, ‘Enough is enough.'”

Mr. Brynien took note of the governor’s refusal to seek the extension of a temporary income tax surcharge on high-earning residents during this year’s legislative session, a position that put Mr. Cuomo at odds with other Democrats and organized labor.

“The state should not be demanding this level of sacrifice from us while it’s not demanding those same sacrifices from the wealthiest New Yorkers,” he said.

Mr. Cuomo has repeatedly threatened that there would be layoffs if state workers did not accept deep wage and benefit concessions; the state has estimated that 3,500 members of the Public Employees Federation would lose their jobs if the union rejected the concessions package.

The state’s largest union of public workers, the Civil Service Employees Association, announced on Aug. 16 that its membership had voted 59 percent to 41 percent to approve a nearly identical five-year agreement that promised job protections in exchange for wage and benefits concessions.

Mr. Brynien asked the governor on Tuesday to return to the bargaining table. Mr. Cuomo did not immediately comment on Tuesday, although his administration had indicated that layoffs would follow almost immediately if the union rejected the deal.