WASHINGTON — President Obama bowed Thursday night to mounting criticism that he had misled the American people about the health care law, apologizing to people who were forced off their health insurance plans by the Affordable Care Act despite “assurances from me.”

In an interview with NBC News, Mr. Obama said that he did not do enough to ensure that the law did not force the termination of insurance policies that people like because they do not meet the law’s new coverage requirements.

“It means a lot to them. And it’s scary to them. And I am sorry that they, you know, are finding themselves in this situation, based on assurances they got from me,” Mr. Obama told Chuck Todd of NBC in an interview in the Diplomatic Room of the White House. “We’ve got to work hard to make sure that we hear them and that we’re going to do everything we can to deal with folks who find themselves in a tough position as a consequence of this.”

For years, Mr. Obama has repeatedly said that Americans who were satisfied with their health insurance plans could keep them even after his health care program took full effect at the beginning of next year. “If you like your health plan, you will be able to keep your health plan,” he said in speeches and at campaign rallies and town hall meetings.