The administration of Suffolk County Executive Steve Bellone said Tuesday it will begin a $12 million lag payroll with the April 14 paycheck after leaders of the Suffolk’s largest union rejected Bellone’s final compromise offer last week.

The lag would eliminate one day’s pay from each two-week paycheck for 20 weeks for 4,800 white- and blue-collar workers who belong to the Association of Municipal Employees.

Workers will get their 10 days in deferred pay when they leave county service, at the salary they are making at the time.

Bellone, while seeking re-election last fall, proposed dropping the lag included in the AME’s last contract and instead called for suspending $12 million in county payments to the union benefit fund that pays for dental, vision and legal services.

Bellone said the fund already had $24 million, or two years’ worth of reserves. Union officials opposed the move, saying it would have caused a permanent loss in funding instead of a temporary deferral.

In a letter sent to workers Tuesday, Bellone said he had offered a final compromise to deal with the “one substantive concern” raised by union leaders. Bellone promised to replenish the $12 million to be taken from the benefit fund this year by repaying $1 million a year over the next 12 years.

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AME officials say Bellone never detailed how the benefit fund would be replenished.

“It looked like a 12-year interest-free loan that could be paid back in the end,” said Dan Levler, AME’s first vice president. “Our members view the benefit fund as a sacred cow and they don’t want to risk anything negative happening to it.”

Bellone, meanwhile, rejected a union proposal calling for workers to defer for one year an already scheduled 3 percent raise, due July 1. However, the plan also called for an additional 2 percent raise on July 1, 2017.

Union officials said the extra 2 percent raise in 2017 is more economical than the more than $30 million extra it would cost for the county to pay back the lag payroll in the long run.

Bellone said he will participate in the lag voluntarily and submit resolutions for a March 22 legislative vote that would extend the lag payroll to executive and legislative aides, along with board of election workers.

Bellone also asked union officials to put his final proposal up for a membership vote.

“Unfortunately, they . . . have refused you that choice,” he said in his letter to employees.

Union officials say they are still willing to talk. “We’re not dismissing anything — we still hope this can be worked out,” said AME president Brian Macri.