WASHINGTON — Unwilling to accept defeat, President Trump insisted on Wednesday that Republicans “have the votes” to dismantle much of the Affordable Care Act, and he predicted that the Senate would vote on legislation to do that in the first three months of next year.

In the meantime, he said, he intends to negotiate with Democrats on a bipartisan health care bill and issue a “very major executive order,” probably next week. Under the order, Mr. Trump said, “people can go out, cross state lines, do lots of things and buy their own health care.”

Millions of people could benefit, he said.

Mr. Trump’s seemingly contradictory comments to journalists mystified members of both parties in both houses of Congress.

Senator John Thune of South Dakota, a member of the Senate Republican leadership, laughed when asked about Mr. Trump’s assertion that the votes were there for health care.