WASHINGTON — The Trump administration rejected on Thursday Idaho’s plan to allow the sale of stripped-down, low-cost health insurance that violates the Affordable Care Act.

The 2010 statute “remains the law, and we have a duty to enforce and uphold the law,” Seema Verma, the administrator of the federal Centers for Medicare and Medicaid Services, said in a letter to the governor of Idaho, C. L. Otter.

While rejecting Idaho’s plan in its current form, Ms. Verma encouraged the state to keep trying, and she suggested that, “with certain modifications,” its proposal might be acceptable.

President Trump has repeatedly criticized and undermined the Affordable Care Act, President Barack Obama’s signature achievement, saying it drove up insurance costs for millions of Americans.