Blue Cross and Blue Shield of Minnesota is proposing rate increases of up to 11 percent for the plans it offers in the public marketplace. Without reinsurance, it said, its rates would rise 16 percent to 32 percent, on average. By contrast, its average rate increase this year was 55 percent.

Hodan Guled, the chief executive of Briva Health, a community group that helps Minnesotans sign up for coverage under the Affordable Care Act, said the reinsurance program was “definitely helpful and beneficial” for consumers.

State Senator Tony Lourey, the senior Democrat on the health committee in the Minnesota Senate, said he voted against the legislation because it was financed mainly with money from a fund intended for a separate state health program for the working poor. But he said, “Reinsurance itself is a good tool, a valuable tool, to mitigate premium spikes, and this program does work.’’

“This is the type of risk-mitigation tool that the feds defunded in an effort to sabotage Obamacare,” Mr. Lourey said. “It’s left to states then to put this massive investment in place. The feds need to be stepping up to the plate and not leaving it to the states.”

The Affordable Care Act created a temporary federal reinsurance program, which was in effect from 2014 to 2016. But like much of the law, it became snarled in politics and legal disputes.

Under the measure adopted this year in Minnesota, the state reinsurance program pays 80 percent of the amount of a claim from $50,000 to $250,000. The insurer is responsible for any amounts over $250,000.

If, for example, a person has $60,000 in claims next year, the reinsurance program would pay the insurer 80 percent of $10,000, or $8,000. If a person has $600,000 in claims, the program would cover 80 percent of the cost from $50,000 to $250,000 — 80 percent of $200,000 — so the payment to the insurer would be $160,000.