Obama's mea culpa came amid a controversy over his repeated assurances that if citizens liked their existing coverage, they could keep it under his signature health care reform, dubbed Obamacare.
But hundreds of thousands of Americans have in recent weeks received notices from their health providers that their policies will be canceled.
"I am sorry that they are finding themselves in this situation based on assurances they got from me," Obama told NBC News in an interview.
The White House says the policies were scrapped because they did not comply with more stringent standards required by Obamacare and that those who lost coverage would be able to buy better plans under new health exchanges.
"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," Obama said in the interview.
Americans worried about losing their health insurance have been frustrated in attempts to sign up for new plans under Obamacare by a glitch-prone website, which sparked chaos after it went live on October 1.
"The majority of folks will end up being better off. Of course, because the website's not working right, they don't necessarily know it," Obama admitted, and said he would do everything he could to end the teething problems.
"I am deeply frustrated about how this website has not worked over the first couple of weeks. And, you know, I take responsibility (for) that."
"My team take responsibility. We are working every single day, 24/7, to improve it."
The Obamacare debacle has mushroomed into a political crisis that has called into question Obama's personal candor and administrative competence and cast a shadow over an already difficult second term.
Republicans who opposed the passage of Obamacare have slammed the president over the poor rollout of the law and plan to use it to undermine Democratic candidates ahead of mid-term congressional elections next year.
"If the President is truly sorry for breaking his promises to the American people, he'll do more than just issue a half-hearted apology on TV," said Republican Senate minority leader Mitch McConnell.
The veteran Republican told Obama that he should support a bill in Congress that has won the support of several Democratic senators as well as many Republicans, that would allow Americans to keep their health care plans in the manner Obama first promised.
Republican House speaker John Boehner also joined the chorus of Obama critics.
"An apology is certainly in order, but what Americans want to hear is that the president is going to keep his promise," Boehner said in a statement, demanding that Obama back next week's bill in Congress.
"If the president is sincerely sorry that he misled the American people, the very least he can do is support this bipartisan effort," he said. "Otherwise, this apology doesn't amount to anything."