WASHINGTON — President Barack Obama says he’s sorry Americans are losing health insurance plans he repeatedly said they could keep under his signature health care law. But the president stopped short of apologizing for making those promises in the first place.

‘‘I am sorry that they are finding themselves in this situation based on assurances they got from me,’’ he said in an interview Thursday with NBC News.

He added: ‘‘We’ve got to work hard to make sure that they know we hear them, and we are going to do everything we can to deal with folks who find themselves in a tough position as a consequence of this.’’

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The president’s apology comes as the White House tries to combat a cascade of troubles surrounding the rollout of the health care law often referred to as ‘‘Obamacare.’’ The healthcare.gov website that was supposed to be an easy portal for Americans to purchase insurance has been riddled by technical issues. And with at least 3.5 million Americans receiving cancellation notices from their insurance companies, there’s new scrutiny aimed at the way the president tried to sell the law to the public in the first place.

Much of the focus is on the president’s promise that Americans who liked their insurance coverage would be able to keep it. He repeated the line often, both as the bill was debated in Congress and after it was signed into law.

But the measure itself made that promise almost impossible to keep. It mandated that insurance coverage must meet certain standards and that policies that fell short could no longer be sold except through a grandfathering process, meaning some policies were always expected to disappear.

The White House says under those guidelines, fewer than 5 percent of Americans will have to change their coverage. But in a nation of more than 300 million people, 5 percent is about 15 million people.

Officials argue that those people being forced to change plans will end up with better coverage and that subsidies offered by the government will help offset any increased costs.

‘‘We weren’t as clear as we needed to be in terms of the changes that were taking place,’’ Obama told NBC. ‘‘And I want to do everything we can to make sure that people are finding themselves in a good position, a better position than they were before this law happened.’’

The president’s critics have accused him of misleading the public about changes that were coming under the law, which remains unpopular with many Americans and a target for congressional Republicans.

Obama dismissed that criticism, saying ‘‘I meant what I said’’ and insisting that his administration was operating in ‘‘good faith.’’ He acknowledged that the administration ‘‘didn’t do a good enough job in terms of how we crafted the law’’ but did not specify what changes might be made.

Sign-ups for the new health care marketplaces opened Oct. 1. People have six months to enroll before facing a penalty.

Some lawmakers — including Democrats — have called on the White House to delay the penalty or extend the enrollment period because of the website woes that have prevented many used from signing up. Obama said he remains confident that anyone who wants to buy insurance will be able to do so.

‘‘Keep in mind that the open enrollment period, the period during which you can buy health insurance is available all the way until March 31,’’ he said. ‘‘And we’re only five weeks into it.’’