The Obama administration tonight significantly relaxed the rules of the health-care law for millions of consumers whose individual insurance policies have been canceled, saying they could now buy bare-bones health plans or entirely avoid the requirement that most Americans have health insurance.

The surprise announcement, four days before the Dec. 23 deadline for people to choose coverage that begins on Jan. 1, triggered an immediate backlash from the health insurance industry.

Robert Zirkelbach, spokeman for American’s Health Insurance Plans, the industry’s main trade group, said

“This type of last-minute change will cause tremendous instability in the marketplace and lead to further confusion and disruption for consumers.”

Federal health officials said that the new rules will allow any consumer whose current, substandard insurance plan is being canceled to claim a “hardship exemption,” if they believe that the health plans sold through the new federal and state marketplaces are more expensive.