The timing of the announcement, just before an election in which the protection of people with pre-existing conditions has been a top-tier issue, was puzzling. In a separate initiative on Monday, the administration said it was proposing a regulation to let employers provide money to employees to buy individual health insurance coverage on their own, rather than enrolling in an employer-sponsored health plan.

Seema Verma, the administrator of the Centers for Medicare and Medicaid Services, who devised the policy allowing states more flexibility, said it was necessary to achieve President Trump’s goals: to make health insurance more affordable by expanding choices, increasing competition, reducing federal regulations and giving states more power to revamp their health insurance markets. She said states had asked for more flexibility.

Under the restrictive guidance issued by the Obama administration in 2015, Ms. Verma said, “states have largely lost the power to advance and adopt their own solutions.” Waivers issued under the new policy “will allow states to get out from under the onerous rules imposed by the Affordable Care Act,” she added.

A provision of the 2010 health law, added at the behest of Mr. Wyden, allows waivers for innovations in state health policy. The federal law stipulates that state programs must provide coverage that is “at least as comprehensive” as that available under the Affordable Care Act, and must cover “at least a comparable number” of people.

Under the new policy, states will be able to count people with short-term insurance as having coverage even though it does not provide all the benefits required by the Affordable Care Act. Such plans often omit coverage for maternity care, prescription drugs and treatment for mental illness and drug abuse. They often exclude coverage for pre-existing conditions, as well.