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 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 reelection 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.

Until now, the law allowed people younger than 30 to buy catastrophic coverage — an exception to the law’s benefit rules in an effort to attract young adults who have been particularly prone to avoiding coverage in the past. The law also has allowed hardship exemptions for people 30 and older who could not afford the regular coverage.

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 ability 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 administration'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 the dozen Democratic senators, who contended that steps the president had taken did not go far enough to help people whose insurance was canceled.

Six of those senators sent a letter on Wednesday to HHS Secretary Kathleen Sebelius, asking for 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, Mark R. Warner (D) and Timothy M. Kaine (D).

The six senators issued a statement Thursday night, saying that they are “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 for the insurance Web site,, it is working smoothly, they said. They also have added 800 trained staff members to their call centers for people who want enrollment advice by phone, so that there are now 12,000 staffers at 17 call centers nationwide.

Paul Kane, Ed O’Keefe, and Juliet Eilperin contributed to this report.