WASHINGTON — The Obama administration on Thursday night significantly relaxed the rules of the federal health-care law for millions of consumers whose individual insurance policies have been canceled, saying they can buy bare-bones plans or entirely avoid a requirement that most Americans have health coverage.

The surprise announcement, days before the Dec. 23 deadline for people to choose plans that will begin Jan. 1, triggered an immediate backlash from the health insurance industry and raised fairness questions about a law intended to promote affordable and comprehensive coverage on a widespread basis.

The rule change was issued in a bulletin from the Department of Health and Human Services. It is the second major response by the Obama administration to a public and political furor that erupted in the fall when several million people who bought their own insurance began to receive notices that their policies were being canceled because they fell short of new benefit standards. The cancellations prompted complaints that President Barack Obama had reneged on an oft-repeated promise that, under the Affordable Care Act, people who like their health plans could keep them.

At a news conference in mid-November, an apologetic Obama relented to the criticism, announcing that the federal government would let insurance companies continue for another year to offer individuals and small businesses health plans that do not meet the new requirements. The decision, however, is up to each state’s insurance regulator, and not all have gone along.

This second change, prompted by a group of Democratic senators – most of whom face tough re-election campaigns next year – goes substantially further in accommodating people upset about losing their policies. The latest rule will allow consumers with a canceled health plan to claim a “hardship exemption” if they think the plans sold through new federal and state marketplaces are too expensive.

The ability to get an exemption means that the administration is freeing these people from one of the central features of the law: a requirement that most Americans have health insurance as of Jan. 1 or risk a fine. The exemption gives them the choice of having no insurance or of buying skimpy “catastrophic” coverage. This means, in turn, that people who had old, meager insurance have greater freedom under the law than the many millions of uninsured Americans who now must obtain coverage.

Until now, the law allowed only people younger than 30 to buy catastrophic coverage if they couldn’t afford a better health plan. The exception was an effort to attract young adults who have been particularly prone to avoiding coverage in the past.

It is unclear how many people facing canceled policies will choose no insurance, bare-bones coverage or a plan through the insurance exchanges that meet new federal standards. But the prospect that healthy people with canceled insurance might opt out of the new health plans set off immediate alarm among insurance industry leaders, who already have been worried whether enough people who are inexpensive to cover will sign up.

“This latest rule change could cause significant instability in the marketplace and lead to further confusion and disruption for consumers,” said Karen Ignagni, president of America’s Health Insurance Plans, the industry’s main trade group.

Another health insurance official, who spoke on the condition of anonymity because he lacked authorization to discuss the matter publicly, pointed out that the hardship exemption also gives one group the abillity to buy coverage whenever they want, rather than during annual open-enrollment periods. As a result, he said, more people might not buy insurance unless they get sick.

Federal health officials estimated Thursday that, of all the people whose substandard health plans have been canceled, less than half a million have not chosen new coverage. But they acknowledged that they were not certain.

The insurance official suggested that some people who have chosen new health plans after receiving a cancellation notice might back out of their new coverage to take advantage of the admnistration’s sudden offer.

Federal health officials, however, predicted that relatively few people would take advantage of the opportunity to avoid the law’s benefits requirement, reasoning that they have had insurance in the past so would probably want it in the future.

“This is a common-sense clarification of the law,” said Joanne Peters, a spokeswoman for the Department of Health and Human Services. “For the limited number of consumers whose plans have been canceled and are seeking coverage, this is one more option.”

The administration’s move is a swift response to about a dozen Democratic senators, all facing difficult re-election attempts next year or from states that Obama lost in last year’s election, who contended that the steps the president already took did not go far enough to help people whose insurance has been canceled.

A half-dozen of those senators, all Democrats, sent a letter on Wedneday to Health and Human Services Secretary Kathleen Sebelius, asking her to allow people whose plans have been canceled to claim hardship exceptions and buy bare-bones, catastrophic coverage. “We have heard from many of our constituents who are upset by the cancellation of the health plans,” said the letter, whose signers include both of Virginia’s senators, Sens. Mark Warner and Tim Kaine.

The six senators issued a statement Thursday night, saying that they were “pleased the administration appears to have responded to the concerns we’ve raised. … We will closely monitor how the administration implements this option, and we remain committed to proposing responsible solutions.”

As administration officials are granting more flexibility to one group of consumers, they also are working to cope with what is expected to be a rush of people signing up for health plans through the new federal insurance marketplace by the Dec. 23 enrollment deadline. After a trouble-ridden first two months, they say that insurance website, HealthCare.gov, is working smoothly. They also have added 800 trained staff to their call centers for people who want enrolling advice by phone, so that there are now 12,000 staffers at 17 call centers across the country.

Washington Post staff writers Paul Kane, Ed O’Keefe, and Juliet Eilperin contributed to this report.