President Obama explained how Americans who wish to keep their health plans can work to do so under his signature health-care law during a speech Friday. (The Washington Post)

Faced with resistance from insurers and some state officials to his health-insurance fix, President Obama hastily summoned insurance industry executives Friday for what he called a “brainstorming” session against the backdrop of widespread anxieties about how the new twist in his health-care law will be carried out.

A day after announcing a plan to delay insurance cancellations in the individual market by one year, Obama is grappling with concerns that the shift could disrupt the market and lead to higher premiums.

So far, two states — Washington and Vermont — have announced that they will not allow their health insurers to extend insurance policies that do not comply with minimum standards set by the 2010 Affordable Care Act, the health-care law widely known as Obamacare.

Three other states — Ohio, Florida and Kentucky — announced that they would allow the renewals. At least eight states and the District of Columbia said they are trying to decide what to do in the wake of Obama’s announcement Thursday, which was intended to deal with a political furor over the cancellation of many Americans’ individual insurance policies because they do not meet the minimum requirements for coverage.

Combined with the botched rollout last month of, the Web site for the new federal health-insurance marketplace, the policy-cancellation uproar has helped undermine Obama’s signature domestic achievement, fueling political attacks by congressional Republicans and angst among vulnerable Democrats.

In a measure of the misgivings on Capitol Hill, 39 Democrats joined most Republicans in the House in voting 261 to 157 Friday to approve a bill that would allow insurance companies to keep selling indefinitely individual health policies that do not meet the law’s basic standards. Obama has vowed to veto the bill, introduced by Rep. Fred Upton (R-Mich.) and called the Keep Your Health Plan Act. The administration argues that the bill would effectively gut the Affordable Care Act’s requirement that, beginning next year, insurance policies cover at least 10 “essential” health benefits — such as maternity care and mental health services — that often are excluded from current private insurance plans.

Speaking to reporters at the start of his meeting with insurance executives, Obama said he and top aides wanted to confer with them on ways to ensure that Americans know what kind of health coverage they can get under the law.

“What we’re going to be doing is brainstorming on how do we make sure that everybody understands what their options are,” Obama said in the Roosevelt Room. “Because of choice and competition, a whole lot of Americans who’ve always seen health insurance out of reach are going to be in a position to purchase it. And because of the law, we’re also going to be able to provide them help even if they are still having trouble purchasing that insurance. But they’ve got to know what those options are in order to be successful.”

Saying that “we know the demand is out there” for health insurance, Obama noted that “despite all the problems with the Web site,” more than 1 million people applied and “many multiples of that wanted to see what options were available.”

“Obviously, because of the problems with the Web site, some folks have been blocked from seeing the well-priced benefits that are available in the marketplace, and so we’re working 24/7 to get it fixed,” he said. “The Web site is working a lot better now than it was a couple of weeks ago.”

Summarizing the meeting afterward, the White House said Obama told the executives that they and the administration “share the same goal: getting more Americans covered.”

“The discussion was productive — the insurance CEOs and administration officials discussed the next steps in working with states and state insurance commissioners to use the new flexibility the administration announced to address cancellation notices going to consumers,” the White House said. “Meeting participants stressed the importance of working together to minimize disruption for consumers as well as the need to continue to reach consumers with clear information about their options and choices.”

Among the 15 executives participating were the CEOs of Aetna, Humana, CareFirst, Kaiser Permanente and the Blue Cross Blue Shield Association. The administration side included Marilyn Tavenner, administrator for the Centers for Medicare and Medicaid Services (CMS); Denis McDonough, the White House chief of staff; and Valerie Jarrett, a senior Obama adviser.

Before Friday’s meeting, top White House officials, including McDonough, had met twice with insurance industry executives since the Oct. 1 launch of the federal marketplace to discuss its troubled rollout, and the administration had consulted with some insurance companies on the president’s proposal before he announced it Thursday.

But the sudden decision to convene a meeting between the president and health-care chief executives highlighted both the level of anxiety within the insurance industry about the administration’s policy fix and the many questions that remain about how it will be carried out.

Obama said Thursday that insurance companies could continue for another year to offer to individuals and small businesses health plans that do not meet requirements under the new law, which set minimum standards for the benefits that policies must cover.

After the president’s announcement, insurers said that although they appreciate Obama’s effort to address consumer concerns, they are worried that the move could distort the risk pool in the new state and federal health-insurance marketplaces. That is because individual policies tend to be significantly more expensive than group insurance, except for customers who are young, healthy and use little medical care — the very people whom federal officials are counting on to join the new exchanges.

“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 Ignani, president and chief executive of America’s Health Insurance Plans. “If now fewer younger and healthier people choose to purchase coverage in the exchange, premiums will increase, and there will be fewer choices for consumers.”

The American Academy of Actuaries was among the groups that immediately warned of negative effects if insurers were to keep offering those previous plans. The White House’s approach is “threatening the viability” of the new insurance marketplaces, said Corri Uccello, the academy’s senior health fellow.

Even if their mix of customers changes as a result of the new rules, insurers cannot change their prices for 2014, because the rates already have been set by each state’s insurance regulator. Senior administration officials said they could not predict what might happen to prices for 2015, when some old individual and small-business policies will still be in effect for much of the year.

State insurance commissioners and other health policy experts made clear that the landscape will vary substantially around the country.

Eight states, including California and New York, recently prohibited insurance companies from continuing to sell individual or small-group health plans unless they meet the new federal standards for coverage.

Within hours of Obama’s announcement at a White House news conference Thursday, Washington’s insurance commissioner issued a defiant statement that criticized the president and said the state would not allow noncompliant policies to be extended beyond the end of the year.

“I do not believe his proposal is a good deal for the state of Washington,” said the insurance commissioner, Mike Kreidler. He said substandard health plans need to end to protect consumers and prevent prices from rising.

“In the interest of keeping the consumer protections we have enacted and ensuring that we keep health insurance costs down for all consumers, we are staying the course,” Kreidler said in a statement.

Arkansas’ insurance commissioner, Jay Bradford, said Thursday that he would not permit the extension. “At this stage, it would be too confusing to our consumers,” he said. “It would be more chaos added to an already chaotic situation.”

But Arkansas backtracked on Friday, saying it was still trying to decide whether to allow the minimal policies to be extended.

In a joint statement with local insurance carriers, Vermont Gov. Peter Shumlin (D) said: “Weeks ago, we made the decision to allow Vermont individuals and small businesses to extend their current plans through March 31, 2014, if they choose. We remain confident in that timeframe and believe it will provide Vermonters the security and options they need as we continue to improve Vermont Health Connect and implement the federally mandated reforms.”

Among the states that are allowing late renewals, Ohio has expressed concern about the “uncertainty and complexity” of the new policy. Nevertheless, Ohio Lt. Gov. Mary Taylor (R) said in a statement, “We support allowing Ohioans to keep the health care plans they want, as they were promised when Obamacare was being explained to them, and we will work with companies to reissue those plans if they choose.”

Kentucky Gov. Steve Beshear (D) said his state “will comply with the president’s request to allow Kentucky’s insurers the option of determining whether to extend existing health insurance policies to current policyholders for one more year.” He added in a statement, “This will be a business decision for each insurer to make.”

States that said they were considering their options include Arkansas, California, Colorado, Idaho, Indiana, Mississippi, Oregon and South Dakota, plus the District of Columbia.

In the D.C. region, Care­First, the area’s dominant carrier, said it is studying Obama’s announcement and will communicate directly with affected policyholders. But CareFirst noted that it is “strictly bound” by state laws. “At the moment, it is unclear whether state laws would preclude us from doing what the president has proposed,” CareFirst said.

In Maryland, for example, state law requires that beginning in 2014, new plans in the individual and small-group market meet the provisions of the Affordable Care Act, including coverage of essential health benefits, such as maternity care.

Sarah Kliff, Ed O’Keefe, Sandhya Somashekhar, Amy Goldstein and Lena H. Sun contributed to this report.