“We strongly oppose any legislation that would allow employers to inquire about employees’ private genetic information or medical information unrelated to their ability to do their jobs, and to impose draconian penalties on employees who choose to keep that information private,” a group of advocates, including AARP, the American Diabetes Association, the American Academy of Pediatrics, the Epilepsy Foundation, the March of Dimes and others wrote in a letter this week to Ms. Foxx.

As wellness programs proliferate across the corporate landscape, workers are increasingly being asked by their companies to undergo health screenings and medical assessments. Employees can opt out of these programs, and personal information specific to a worker is not supposed to be shared directly with the company. The prohibition is aimed at preventing someone from being fired or otherwise discriminated against because of a serious medical condition.

The federal Equal Employment Opportunity Commission has vigorously pursued legal action against some employers it claimed went too far and used these programs inappropriately, but the courts have largely been sympathetic to the employers’ arguments. Companies also complained that the regulations were confusing, and the commission issued final rules in May aimed at addressing some of their concerns.

Companies defend the wellness programs, saying they keep workers healthier and help reduce insurance costs. But some studies have questioned the effectiveness of these initiatives.

Critics argue that workers are essentially being coerced into giving up private medical information, such as their weight, their blood pressure and whether they are at particular risk for cancer. Under the Affordable Care Act, employers can entice a worker by offering as much as a 30 percent reduction in insurance payments. Although the financial incentives offered have typically been lower, an employee who refused to participate could lose as much as thousands of dollars in savings.