WASHINGTON — Faced with resistance from insurers and some state officials to his health-insurance fix, President Obama 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 they will not allow their health insurers to extend insurance policies that do not comply with minimum standards set by the Affordable Care Act.

Three other states – Ohio, Florida and Kentucky – announced they would allow the renewals. At least eight states 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.

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 called the Keep Your Health Plan Act introduced by Rep. Fred Upton, R-Mich. The administration argues that the bill would effectively gut the ACA 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 insurance plans.

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.

“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,” Obama said.

After the president’s announcement Thursday, 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 health-insurance marketplaces.