"Insurers can extend current plans otherwise canceled in 2014," Obama said in a nearly hourlong statement and news conference Thursday.
The final decision would rest with insurance companies, who could offer canceled plans but wouldn't be required to do so.
"We're also requiring insurers to extend current plans to inform their customers about two things. One, what protections these renewed plans don't include," Obama said. "No. 2, that the marketplace offers new options with better coverage and tax credits that might help you bring down the cost."
He encouraged those who received a cancellation letter to look at the marketplace.
"Even if the website isn't working as smoothly as it should be for everybody yet," he said, "the plan comparison tool that lets you browse costs for new plans near you is working just fine."
Senate Majority Whip Dick Durbin, D-Ill., said in a statement the administration's plan to allow insurers to offer consumers the option to renew their 2013 health plans in 2014 was adequate.
"This decision is sensible and provides the small number of affected consumers with more information and choices about their healthcare. There is no need for a legislative fix for this issue," Durbin said, calling on Congress to work with the administration to improve implementation of the law.
House Speaker John Boehner, in a statement, said Obama's announcement seemed to be "little more than a political response designed to shift blame rather than solve the problem. This problem cannot be papered over by another ream of Washington regulations."
The administration has been slammed for the botched rollout of a core component in the Affordable Care Act, aka Obamacare: healthcare.gov, the federal website that allows visitors to compare, shop and buy health insurance.
"We fumbled the rollout of the healthcare law," Obama admitted.
Saying technical glitches with the website and a broken pledge that Americans could keep their health insurance were "on me," the president said he heard "loud and clear" about the mounting frustration with the law.
"We have to ask ourselves some hard questions inside the White House why we didn't see more of these problems coming on," the president said.
President Obama said he wasn't informed "correctly" about all the problems with the website and said if he knew the breadth of the problems he wouldn't have compared shopping on healthcare.gov to the shopping experience on Amazon or Travelocity.
He repeated his apology to the American people for all the problems with the rollout, saying he recognized he had to re-earn their trust.
"I'm just going to keep on working as hard as I can around the priorities that I think the American people care about," Obama said. "And I think it's legitimate for them to expect me to have to win back some credibility on this healthcare law in particular and on a whole range of these issues in general."
He again acknowledged his unequivocal and oft-repeated "If you like your current policy you can keep it" mantra "ended up not being accurate."
"It was not because of my intention not to deliver on that commitment and that promise," Obama said. "We put a grandfather clause into the law, but it was insufficient."
He said he was considering the entire health insurance universe that includes employer-sponsored plans, Medicare and Medicaid coverage besides individual coverage, which he said accounted for about 5 percent of policies. He also said he believed grandfathering in insurance coverage in effect before the healthcare law went into effect would be adequate.
"My working assumption was that the majority of those folks would find better policies at lower costs or the same costs in the marketplaces, and that [for] folks who potentially would not find a better deal in the marketplaces, the grandfather clause would work sufficiently for them," Obama said.
"And it didn't."
He wouldn't commit that "100 percent of the people" would experience a seamless, smooth experience "100 percent of the time" come Nov. 30-Dec. 1, when administration officials promised a better experience for the majority of those who visit healthcare.gov.
Obama said he had an obligation to the American people and to those in Congress who supported the Affordable Care Act to fix it.
Obama said there was "no doubt" that "our failure to roll out the ACA smoothly has put a burden on Democrats, whether they're running or not, because they stood up and supported this effort through thick and thin."
Astronomers offer more expansive view of universe
Attkisson leaves CBS News, reportedly over network's 'liberal bias'