ST. PAUL — Minnesota booked nearly $650 million in savings by tweaking how it handles subsidized health care programs, state officials announced Tuesday.

Health care costs were a major issue in the Legislature this year as GOP lawmakers sought drum up hundreds of millions in dollars in savings by weeding out fraud from the state’s public programs and dismantle the health care plan for the working poor altogether..

Those plans didn’t pan out, but Minnesota saved almost $450 million by putting its contracts with health plans to cover more than 800,000 low-income residents through competitive bidding, Department of Human Services Commissioner Lucinda Jesson said.

The state first started bidding those contracts out in 2011 in Minnesota’s seven-county metro area. The new coverage for MinnesotaCare and Medical Assistance — Minnesota’s version of Medicaid — in 2016 will be the first to go through competitive bidding across the entire state.

It’s a route that the state should have taken from the start, Gov. Mark Dayton said.

“It’s a great thing for taxpayers,” Jesson said Tuesday. “It’s a huge stride.”

The state will also get an additional $200 million windfall from health plans, who expected the flood of new enrollees triggered by President Barack Obama’s health care law to be sicker — and therefore more expensive — than what panned out.

A majority of the $650 million in savings will go back to the federal government, which helps cover a large portion of the cost of the state’s public programs.