ALTOONA, Iowa — Sen. Bernie Sanders announced a key change to his Medicare-for-all insurance plan Wednesday, a move meant to assuage fears on the part of organized labor, whose support is being heatedly sought by all of the candidates for the Democratic presidential nomination.

Labor representatives have expressed concerns to candidates publicly and to campaign staffs privately that a single-payer system could negatively affect their benefits, which in many cases offer better coverage than private plans. The change announced Wednesday would effectively give organized labor more negotiating power than other consumers would have under his plan by forcing employers to pay out any money they save to union members in other benefits.

One of the primary concerns union members and leaders have raised about Sanders’s Medicare-for-all plan is that they negotiated health-care coverage under the current system, in some cases ceding salary in exchange for those benefits.

Under Sanders’s new wrinkle, those unions could renegotiate their contracts under the supervision of the National Labor Relations Board. “Unions will still be able to negotiate for and provide wrap-around services and other coverage not duplicative of the benefits established under Medicare-for-all,” the plan now says, a seeming acknowledgment of a role for private coverage by a campaign that has railed against others for not taking a hard-enough stance against such plans.

A Sanders aide — who spoke on the condition of anonymity to explain the change — said the provision “does not open a door for private insurance,” which the senator argues would have an extremely limited role under his plan, covering procedures such as plastic surgery. Campaign adviser Jeff Weaver said the change is meant to guarantee that any savings to employers under the Medicare-for-all plan “must be passed on to their organized workers in the form of additional wages or benefits.”

Still, the provision represents a departure for Sanders.

“We are talking to the unions, obviously. You’re looking at perhaps the strongest pro- union member of the United States Congress; we’re going to work with unions on this issue,” Sanders told reporters after his remarks Wednesday.

“What they will be able to do is take health care off the table, because their members will have comprehensive health care as a human right, as well, every other American and then they can sit down and negotiate for decent wages and decent benefits.”

The plan comes as many of Sanders’s opponents are loosening their embrace of his Medicare-for-all plan — even those who had endorsed it. Earlier this year, Sen. Kamala D. Harris (D-Calif.), a Medicare-for-all supporter, brushed aside concerns that it would largely replace private insurance. But as polls began demonstrating that many voters wanted that option to remain, she and others began adjusting their insurance plans.

“I don’t think it was any secret that I was not entirely comfortable — that’s an understatement,” Harris said in a recent interview with The Washington Post. “I finally was like, ‘I can’t make this circle fit into a square.’ ”

Former vice president Joe Biden and a few other candidates have vocally spurned Medicare-for-all, insisting that a better alternative is improving the Affordable Care Act pushed through by Democrats during the Obama administration.

Sanders and his staff have cast the Vermont independent as the purest liberal in the field, the only one with an unwavering commitment to undoing the influence of private health insurance companies and benefiting unions. Yet questions about the impact of his health care plan have continued to arise. On Monday, at a labor town hall in Davenport, Iowa, a United Automobile Workers member wearing a hard hat stood up to challenge him.

“You want to put us on a socialized health care and get taxed more for it when we get it for free, basically, from our employers,” the man said. “which I worry about because . . .”

Sanders interrupted him.

“What was your wage increase this year?” he asked. The man said he had just been hired, at which point Sanders interrupted him again, and explained why the worker would no longer need private insurance under Medicare-for-all.

“The program I’m advocating will be far more comprehensive than the program you have. There will be no deductibles, no co-pays,” Sanders said, adding that unions could shift their focus to “wages and working conditions and pensions.”

That voter wasn’t the first person to ask Sanders about union benefits that morning, let alone during the campaign.

When Sanders appeared Wednesday at an Iowa Federation of Labor conference in Altoona, the sensitivity of the issue was obvious: Even as he detailed many elements of his health-care plan, he did not discuss how union benefits would be handled as part of a transition to Medicare-for-all, telling the room of union members he didn’t have time for all the details.

Kelli Harrison, 54, a political coordinator for the UAW who is undecided in the race, said later that “I kind of like my own insurance . . . and I don’t want to lose that, because who knows how they’ll roll it out.” She, like Biden, preferred working to improve the Affordable Care Act. “They worked so hard to get there. I don’t know if I want to say, ‘Let’s just throw it away and start with something else.’ I don’t think that’s realistic.”

Biden has been endorsed by one high-profile union, the International Association of Fire Fighters, but many others have yet to back a candidate. Bethany Khan, a spokeswoman for the Culinary Union, which represents about 60,000 hospitality workers in Nevada and whose endorsement is coveted, said her union’s leaders have met with Sanders, Harris, Sen. Elizabeth Warren (D-Mass.) and others.

“We’re telling them that the unions don’t want to lose their health care,” Khan said. “It’s built by workers and run by workers.”

Warren, the candidate whose catchphrase is “I have a plan for that,” has yet to announce a health-care proposal.

“I’m with Bernie on Medicare-for-all,” Warren said in the first Democratic debate in July. She did not bring up specifics about Medicare-for-all when she addressed the Iowa Federation of Labor on Wednesday.

Not all union leaders and membership are troubled by Medicare-for-all.

“If we don’t have to negotiate health care in our contracts anymore, that allows us to bargain for other things, whether it’s an increase in pensions, an increase in hourly wages,” said Dallas Tully, a 39-year-old UAW member who caucused for Hillary Clinton in 2016.

Sara Nelson, international president of the Association of Flight Attendants, also agrees with Sanders.

“For-profit health care is getting more and more expensive. Management is coming to the table with proposals that shift more costs to the employees, to downgrade coverage, to take away plans. It’s a huge battle,” Nelson said. “Even if you have a great plan, one of these so-called ‘Cadillac’ plans, you’re in a for-profit system . . . and the experience in this health-care system continues to be degraded.”

Nelson said she could see her union negotiating for benefits covered by private insurance companies in addition to what is covered by Medicare-for-all. The Sanders campaign has always said, and did so again Wednesday, that under Medicare-for-all such coverage would not be necessary.