The Obama administration announced Wednesday that Americans who want to keep their old health plans may do so for two years longer than they expected, even if the policies don’t comply with the law.

The decision marks the second time in four months that administration officials have adjusted their rules about health plans that do not include benefits required by the 2010 Affordable Care Act.

In the fall, a few million consumers discovered that their noncompliant policies were about to be canceled. A political furor erupted, with accusations that President Obama had broken his promise that people could keep their current insurance.

Obama relented in November, giving states latitude to allow policies to be sold through October, regardless of whether they contain all the benefits required by the law. About half the states have agreed to allow this.

Now, Obama’s health-care aides announced that these old policies may be sold for two years longer, according to the official, who spoke on condition of anonymity about a decision that has not been made public.

HHS spokeswoman Joanne Peters pointed out Tuesday that when the president announced the first extension, health officials had said they would consider further extending the ability to renew old plans beyond this year.

Peters said in a statement: “The Administration has committed to doing all we can to smooth the transition for hard-working Americans. We’ve taken steps already and are continuing to look at options.”

Congressional Republicans who have been trying to derail the law did not wait for the administration’s announcement to begin their criticism. “Another day, another delay,” House Energy and Commerce Committee Chairman Fred Upton (Mich.) said, adding that “unilateral delays and administrative changes to the . . . law have become commonplace.”

This story has been updated.

Juliet Eilperin contributed to this report.