Move will allow people with existing policies that do not meet minimum Obamacare standards to keep them for another year

Barack Obama admitted that he had "fumbled" the rollout of his cornerstone healthcare reforms on Thursday, seeking to defuse a growing revolt among Democrats with an announcement that insurers could to continue offering policies that fall short of new standards for coverage.

The move is aimed at stemming a tide of cancellation letters sent to an estimated the 3.6 million Americans since new rules were introduced under the Affordable Care Act on October 1. Obama said the amnesty for policies that do not meet the act's minimum standards will last for a year.

Democrats in Congress, hit with a wave of complaints from angry constituents, had been pressuring for a change in the law to the deal with the problem.

An apologetic Obama said he needed to “win back the confidence of the American people” after the problems. “It's legitimate to expect us to have win back some credibility on this healthcare law and other issues ... we fumbled the rollout,” he told reporters at a White House news conference.

Under the so-called "administrative fix":

• Insurers will be allowed to extend plans that do not comply with the Affordable Care Act for a year.

• As a condition, they must tell customers of other options available through the troubled online marketplace at the core of the reforms.

• Customers who do not already have such plans will not be able to sign up for them.

• Insurers will not be obliged to extend the sub-standard policies and state insurance commissioners will have the power to block the fix.

The administration hopes it will be enough to satisfy Democrats who had been supporting a similar proposal in the Senate proposed by Mary Landrieu. Obama conceded the botched rollout of the Affordable Care Act was politically damaging for his party. "There is no doubt that the failure to roll out the ACA smoothly has placed a burden on Democrats whether they are running for office or not. We are letting them down and I don't like doing that," he said.

Republicans claimed the one-year delay was a cynical attempt to postpone the issue until after the mid-term elections and repeated calls for the law to be repealed. John Boehner, the Republican speaker of the House of Representatives, said of Obamacare: "It is going to destroy the best healthcare delivery system in the world." The country needs to "scrap this law once and for all," he added. "There is no way to fix this."

Boehner said "reasonable Democrats" are working with Republicans "to give the American people the opportunity to keep the plan they have, and the plan they like."

White House officials presented their solution on Thursday as a short-term administrative action that did not require legislation. But Republicans are still expected to demand more sweeping changes to the ACA in a bill that comes before the House of Representatives on Friday.

It remains unclear whether insurers or state regulators – who will receive a letter informing them of the so-called “enforcement discretion” – will actually act in ways that stop the cancellations. Officials conceded they had received no such guarantees from either states or insurers, many of whom were hoping to use the new law as a way to move customers onto higher-cost policies.

The White House also admits the climbdown may affect the economics of its already troubled healthcare exchanges, by delaying the anticipated influx of new customers that were expected to drive down average costs. An official said it would use a unspecified “stabilising mechanism” to try to avoid a wider rise in premiums on the exchanges.

This is already a concern after software problems led to much lower-than-expected enrolment on the exchanges during their first month.

Insurers warmed that Thursday's announcement could lead to higher premiums and uncertainty in the marketplace. Karen Ignagni, president of America’s Health Insurance Plans, an industry lobby group, said: “Changing the rules after health plans have already met the requirements of the law could destabilize the market and result in higher premiums for consumers. Premiums have already been set for next year based on an assumption of when consumers will be transitioning to the new marketplace.

"If due to these changes fewer younger and healthier people choose to purchase coverage in the exchange, premiums will increase in the marketplace and there will be fewer choices for consumers." She said that the administration would have to take "additional steps" to stabilise the marketplace.

Before the Affordable Care Act was passed, Obama promised that people could “keep their plans if they liked them”. In recent weeks, Obama has faced intense pressure for making a promise that turned out to be false: in fact, his statement only applied to policies that were taken out before the act was passed in 2010 and had not changed since.

“I completely get how upsetting this can be particularly after they heard assurances from me that if they liked their plan they can keep it," Obama said on Thursday. He also hinted that further legislation might be necessary even with the one-year delay. “This fix won't solve every problem every problem for every person; that might require working with Congress.”

But the president insisted that his promise that people could “keep their plans” reflected a miscalculation rather than a deliberate policy. “There is no doubt that the way I put that forward so unequivocally, ended up not being accurate.”

Obama also denied that he had been warned in advance of the separate problems with the online marketplace. “I don't think I'm stupid enough to say 'this is like shopping on Amazon or Travelocity' a week before it was launched, if I didn't think it was going to work."

But the president insisted these were all short-term issues. “I am confident that by the time we look back on this next year, people will say it's working well,” he said.