He also offered no explanation of how he would persuade Congress to pass his plan, though he indicated that it would have the backing of the House speaker, Paul D. Ryan of Wisconsin, and the Senate majority leader, Mitch McConnell of Kentucky. Mr. Trump said only that “I won’t tell you how, but we will get approval.”

He seemed to refer to his recent Twitter posts that helped persuade House Republicans to back away from a proposal to gut an ethics office. “You see what’s happened in the House in recent weeks,” he said.

Top aides to Mr. Trump declined to provide more information about the president-elect’s plans. In an interview last week with The New York Times, Mr. Trump said he wanted Congress to repeal the Affordable Care Act and replace it “very quickly or simultaneously, very shortly thereafter.”

The president-elect told The Post that his plan would be unveiled soon after the Senate confirmed Representative Tom Price, Republican of Georgia, to be the secretary of health and human services.

Achieving the promise of “insurance for everybody” has been a goal of health care policy experts for decades, but the political and financial realities have proved problematic. Government-provided health insurance, known as a single-payer plan, has found little political support in Washington. And market-based solutions, like the Affordable Care Act, have proved difficult to carry out.