Americans who kept their health plans that didn’t comply with Obamacare requirements will be able to renew those policies for two more years, according to a person familiar with the matter.

The Obama administration, which has been deliberating the issue since November, is expected to announce Wednesday the extension of the health plans, said the person, who asked not to be identified because the decision wasn’t yet public.

Insurers sent letters to policyholders canceling the health plans as the new government exchanges opened Oct. 1. The letters caused a political headache for President Obama, who had promised during the debate on the Patient Protection and Affordable Care Act that people who liked their health plans wouldn’t have to change them. About 2.6 million Americans received the cancellation notices, according to a study published March 3 by the journal Health Affairs.

Amid the growing criticism, Obama announced Nov. 14 that state insurance commissioners could allow insurers to extend policies that didn’t comply with the law. Insurance company executives have said they expected the White House would allow renewal of the plans, which don’t comply with rules such as offering coverage for maternity care or limiting out-of-pocket spending.

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The extension affected only a small slice of the U.S. insurance market, people who bought individual health plans for themselves and their families rather than receiving coverage through a company’s group plan or a government program such as Medicare. The Kaiser Family Foundation estimated the plans covered about 5 percent of Americans.

“The administration has committed to doing all we can to smooth the transition for hardworking Americans,” Joanne Peters, a spokeswoman for the U.S. Health and Human Services Department, said Tuesday in an email. “We’ve taken steps already and are continuing to look at options. HHS said in November that we would consider extending the option for Americans to renew old plans beyond this year and we will provide final guidance on this issue soon.”

About 4 million Americans so far have signed up for new coverage in insurance exchanges established by the health care law known as Obamacare. Insurers participating in the exchanges aren’t allowed to refuse coverage to sick people or charge them more than healthy customers. For that reason, companies need many young and healthy Americans to buy plans from the exchanges to balance the cost of covering sick people and avoid premium increases.

People who stayed on old plans, which don’t carry the Affordable Care Act’s consumer protections, are believed to be younger and healthier in general than people on exchange plans. The insurer Humana Inc. said in January that its exchange customers would be sicker and older than it expected in part because Obama allowed renewals of old plans.

Allowing the plans to be renewed “is sort of anathema to the rest of Obamacare,” Gorman said. At least 28 states allowed plans to be extended under Obama’s policy, according to the Commonwealth Fund, a New York foundation that studies health policies.