The New Hampshire Department of Administrative Services is proposing a sweeping overhaul of the state’s retiree health care plan, seeking to switch users into a Medicare program that officials say could help the state save $11.8 million through 2020.

The proposal, presented to the Executive Council on Wednesday, would move the state’s 9,600 Medicare-eligible public retirees off their present plan — a state-funded program called “Medicomp” — and onto a federal initiative known as Medicare Advantage.

That move would allow the state to take advantage of a higher federal match rate under Medicare Part C, the Medicare Advantage program. The proposal would reduce projected costs from January 2019 to December 2020 from $41 million to $29.2 million, according to the department.

Anthem health insurance would continuing administering care for retirees, but under a new funding structure overseen by the federal government.

The proposal comes as the state has struggled to keep up with rising health care costs in its retiree health plans, forcing legislators to address multiple budget shortfalls in recent years, according to the department.

Presenting the plan, DAS Commissioner Charlie Arlinghaus called it an opportunity to save money and keep the program viable. And he said no patient would lose his or her doctor or experience a change in benefits.

“The doctors you will be able to go to are anyone who takes Medicare,” he said. “Which, theoretically, if you’re already in the Medicare program, that’s who you’re using now.”

Under the proposal, Medicare-eligible retirees would receive insurance through Anthem, which in turn would be reimbursed by the federal Centers for Medicare and Medicaid Services on a per-person basis.

The rate would be determined by the health of the people being served and the quality of the care offered, incentivizing Anthem to improve its service, according to the department. By working under Part C of the Medicare program, retirees would benefit from a coordination between Medicare parts A and B, which cover hospital expenses and provider costs, respectively, and Part D, which covers pharmaceuticals.

“Other than the increased attention to the care retirees are receiving, members should experience minimal disruption while continuing with the same level of medical coverage with the flexibility to see the same Medicare participating providers they see today,” Arlinghaus wrote in a letter accompanying the proposal.