Andrea L. Devoti, chairman of the National Association for Home Care and Hospice, said the new rule “will mean that people will receive less care.” She said the higher costs resulting from the new rule would lead many people to hire home care aides part time rather than full time. “Caregivers will in the end receive less pay,” she said.

The newly issued rule was also criticized by Representative John Kline, a Minnesota Republican who is chairman of the House Education and the Work Force Committee, and Representative Tim Walberg, a Michigan Republican who heads the panel’s subcommittee on work force protections.

They said it not only would raise costs, but would “limit access to in-home care for vulnerable Americans.” They added, “Faced with higher costs, some individuals will have no choice but to leave their homes and enter institutional living.” Long-term nursing home care, much of which is paid by Medicaid, is generally more expensive than home care.

Ms. Fortman of the administration’s wage and hour division said 15 states now provided overtime and minimum wage protection to home care aides. “We have not seen any evidence that it has resulted in job loss or any serious negative impact for the workers or for the people using the services,” she said.

The administration announced the change 21 months after first proposing the rule and after having received 26,000 public comments, many of them from for-profit home care agencies that opposed it. Many labor advocates criticized the administration for taking so long to issue its final rule, but Labor Department officials said reviewing the comments and holding related public meetings took time.

The federal government says six million of the 40 million Americans older than 65 need some form of daily assistance to live outside a nursing home. Federal officials estimate that the number will double to 12 million by 2030.

Under the new rule, any home care aides hired through home care companies or other third-party agencies cannot be exempt from minimum wage and overtime coverage. The exemptions for aides who mainly provide “companionship services” — defined as fellowship and protection for an elderly person or person with an illness, injury or disability who requires assistance — are limited to the individual, family or household using the services.