WASHINGTON — Answering criticism from opponents of the Affordable Care Act and members of his own party, President Obama announced this month that health insurance plans that were canceled because of the ACA can be renewed for another year.

The cancellations, most effective on January 1, were widely denounced, partly because the president had promised many times that Americans could keep existing coverage.

Obama said he understood how upsetting it was for policyholders to get a cancellation notice, “particularly after assurances they heard from me that if they had a plan that they liked they could keep it. … To those Americans, I hear you loud and clear. I said that I would do everything we can to fix this ­problem.”

He added that the renewal offer “won’t solve every problem for every person, but it will help a lot of people.”

The offer notwithstanding, he said people facing cancellations should examine options on state and federal insurance exchanges that may be cheaper and offer more coverage.

Acknowledging the “rough” rollout of the federal exchange website, he said that had he been aware of the depth of HealthCare.gov’s problems, it wouldn’t have been launched on October 1. “You know, I’m accused of a lot of things, but I don’t think I’m stupid enough to go around saying, ‘This is going to be like shopping on Amazon or Travelocity,’ a week before the website opens, if I thought that it wasn’t going to work. So, clearly, we, and I, did not have enough awareness about the problems in the website.”

The renewal offer did not appease Republicans, including House Speaker John Boehner of Ohio, who said, “After finally acknowledging he repeatedly misled the American people to sell his health care law, the president is asking Americans to trust him again. The president has absolutely no credibility on his promise. True to form, it appears this is 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. Americans losing their coverage because of the president’s health care law need clear, unambiguous legislation that guarantees the plan they have and like will still be allowed.”

A day after the president’s announcement, the House passed legislation that lets insurers sell for another year health policies that don’t meet ACA requirements. The vote was 261-157, with 39 Democrats breaking ranks to join the GOP majority.

“Working families across America were counting on the president to keep his promise,” majority leader Eric Cantor, (R., Va.), said before the vote. “Now, they are counting on us to ease some of the pain that his health care law has brought them.” Obama’s move also did not go over well with insurers, who questioned the cost and complexity of reinstating policies. “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,’’ said Karen Ignagni, chief executive officer of America’s Health Insurance Plans.

State insurance regulators also had misgivings. “This decision continues different rules for different policies and threatens to undermine the new market,” said Louisiana insurance commissioner Jim Donelon, who is also president of the National Association of Insurance Commissioners.

“In addition, it is unclear how, as a practical matter, the changes proposed by the president can be put into effect,” he said. “In many states, cancellation notices have already gone out to policyholders and rates and plans have already been approved for 2014. Changing the rules through administrative action at this late date creates uncertainty and may not address the underlying ­issues.”

In the Senate, a proposal that would let Americans keep their current health plans permanently was gaining support under an effort spearheaded by Democrat Mary Landrieu of Louisiana, who faces a tough reelection battle next year. Landrieu said she remained committed to her bill, despite the administration’s reluctance to embrace a legislative fix.