WASHINGTON -- With millions of consumers getting cancellation notices for their current health plans, President Obama announced Thursday that he will encourage insurance companies to continue offering their customers the same health plans next year.

“This fix won’t solve every problem for every person,” Obama said, saying he would consider legislative action to go further. But he appeared to rule out the sort of legislation that House Republicans are pushing, which would allow insurance companies to continue selling new policies, indefinitely, that would not comply with the law’s new consumer standards.

“I will not accept” legislation that would “drag us back to a broken system,” Obama said.

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The move comes amid rising outrage over the cancellation notices, which insurers have sent out to customers nationwide who do not have health plans through an employer. Many of these plans do not comply with the Affordable Care Act, which was supposed to require health plans sold next year to offer consumers a new basic set of benefits.

Obama conceded that the problems with the rollout of Obamacare have hurt his standing with Americans, saying he has to “win back some credibility” on the issue.

“We fumbled the rollout on this healthcare law,” he said.

But he said that he was unaware that the federal online marketplace -- healthcare.gov -- was riddled with technological flaws before it went live on Oct. 1. "I was not informed directly that the website was not working the way it was supposed to," he said.

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The president said the website would be working better by Nov. 30, the administration’s self-imposed deadline to fix it, but added, “It is not possible for me to guarantee that 100% of the people 100% of the time will have a perfectly seamless and smooth experience.”

Obama said he understood why consumers who received cancellation notices from insurers were upset. “It’s scary,” he said. But he also noted that the existing market for individual insurance was flawed. "If you received one of the letters, I encourage you to take a look at the marketplace,” he said.

The president also took a far more sober tone than he had in the past about the difficulties involved in buying insurance. “Buying health insurance is never going to be like buying a song on iTunes,” he said, noting the complexities of comparing insurance plans. In the months preceding the rollout of the new law, Obama repeatedly compared the process to using websites such as Amazon or Kayak.

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White House officials said Thursday that new plans sold next year would still have to offer the new benefits, which include hospitalizations, mental health services and maternity coverage.

But the officials said insurers would be free to offer their customers the option to remain on their current plans rather than switching to the new plans, which in some cases are more expensive.

If insurers offer this option, however, they would be required to notify consumers which benefits their current plans are missing. Insurers would also have to alert their customers that other options might be avaliable on the new marketplaces created by the Affordable Care Act.

It is unclear how many insurers would opt to extend current plans. Industry officials have said that doing that would be burdensome.

The White House move, which officials characterized as a “transition,” would not allow health insurers to sell current plans to new customers next year. House Republicans have been pushing for this, which most health experts believe would effectively destroy the new marketplaces created by the health law.

The proposal from Rep. Fred Upton (R-Mich.) would allow health insurers to continue offering health plans next year that do not include new consumer protections and basic benefits required by the health law.

Most people who have these plans now are very healthy, because insurers have been able to deny coverage to consumers who are sick or have been ill in the past. That means that only sicker consumers, who have not been able to get coverage in the past, would likely select health plans offered on the marketplaces created by the health law.

Insurance premiums in turn would spike, making coverage increasingly unaffordable for the sickest people, while healthy people would be able to hold onto their existing health plans.

The president was under intense pressure from Democrats on Capitol Hill to find a fix. Democratic unity crumbled as lawmakers were pounded by their constituents over the rocky rollout of Obamacare, especially as many of them begin tough re-election battles.