ST. PAUL — Gov. Mark Dayton said Thursday he believes President Barack Obama made the right decision by letting insurance companies continue to offer health plans to their customers that were set to be canceled under federal health care changes.

Dayton said at a news conference that Obama “deserves great credit for keeping his promise to the American people.” He said Obama’s one-year extension would give consumers more time to make the right decisions about health insurance.

The prospect of insurance plans cancellations as a result of the federal health overhaul had generated growing criticism in recent days. Dayton said Tuesday that he believed people should be able to keep their insurance. Obama announced the policy shift on Thursday, in a press conference where he acknowledged his administration had “fumbled” the rollout of the federal law so far.

Minnesota’s Department of Commerce, which regulates insurance companies, released a statement saying it was working on implementing the shift.

Minnesota law prevents insurance companies from canceling policies outright. But in recent weeks, at least 140,000 Minnesotans received letters from their insurance companies saying their policies were likely to change significantly because of the federal health care law.

Geoff Bartsh, vice president at Minnetonka-based Medica, one of Minnesota’s largest private insurers, said the company needed time to figure out the ramifications of Obama’s announcement. But he said that “on first glance, the challenges and risks to the insurance market of trying to do this are substantial.”

Insurance companies counted on profits from selling new coverage plans to healthy people, he said, to offset losses from selling plans to people with existing health problems. If large numbers of healthy people are allowed to keep existing plans, “then the products for sick people are all of a sudden woefully underpriced,” he said.

“The insurance industry, and our regulators at the state level, have been working really hard for the past three years to try to make sense of this new law, and to make sure there are responsible products that reflect the new rules,” Bartsh said. “This is sort of turning all that work on its head.”

Bartsh said it would be extremely difficult to retool plans and pricing between now and Jan. 1, when coverage under the federal law is supposed to take effect.

Representatives from the state’s three other largest private insurers did not immediately return calls seeking comment. Those companies are Blue Cross Blue Shield, HealthPartners and Preferred One. Eileen Smith, spokeswoman for the Minnesota Council of Health Plans, said the group would be seeking a meeting with state regulators to discuss next steps.

Not all state officials were as welcoming to the news as Dayton. In Washington state, which is also operating its own health insurance exchange, Democratic Insurance Commissioner Mike Kreidler said he wouldn’t allow insurance companies to extend old policies that didn’t meet the requirements of the federal law. He said most of the people whose old plans are being canceled would be able to find superior coverage through the state exchange.