The state’s largest public-employee union, acknowledging the pressures on government workers around the nation, agreed on Wednesday to major wage and benefits concessions in a pact to avoid sweeping layoffs.

The five-year agreement between Gov. Andrew M. Cuomo, a Democrat, and the Civil Service Employees Association, includes a three-year wage freeze, the first furloughs ever for state workers and an increase in the amount employees must pay toward their health insurance.

Savings would amount to $73 million this year, and as much as $1.6 billion over five years, if other labor unions representing public workers agreed to similar concessions. Absent those agreements, there could still be layoffs of some public workers, the Cuomo administration said.

The agreement was announced as the governor and lawmakers negotiated over a number of issues in the waning hours of the legislative session. Senate Republicans had not decided on Wednesday night whether to allow a vote on the most contentious issue, the proposed legalization of same-sex marriage.

The negotiations between Mr. Cuomo and the union, which represents about a third of the 186,000 state workers, were largely free of the public rancor that accompanied efforts to reduce spending on labor in New Jersey and Wisconsin.

“I want to applaud C.S.E.A. for understanding, truly, the situation that the state is in,” the governor told reporters on Wednesday night. “The union really stepped up and helped the state out at a very precarious time, from a financial point of view.”…..

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