He also said he would be speaking with sports franchise owners like Robert K. Kraft, the owner of the New England Patriots, and sport industry leaders like Adam Silver, the commissioner of the National Basketball Association. “I’m tired of watching baseball games that are 14 years old,” he said. “But I haven’t actually had too much time to watch.”

Mr. Trump was vague about whether those on his list had all agreed to serve on the task force his administration has been struggling to put together over the past week. Some business leaders have been hesitant to attach their names to it in the middle of intense discussions in the White House about who would serve on a formal council, and what its mandate would be.

It was also not clear if all of the companies and executives Mr. Trump mentioned had been asked in advance if they would serve in advisory roles to the White House. At least one person on the president’s list, who asked not to be identified for fear of angering the White House, said that no request had been made to join the list and that there had been no advance notice of an announcement.

Later, the White House sent out a news release outlining names that would serve in 17 “Great American Economic Revival Industry Groups,” which it said would work with it “to chart the path forward toward a future of unparalleled American prosperity.”

The list included a surprising name that Mr. Trump did not mention during his news conference on Tuesday: Jeff Bezos, the Amazon founder who owns The Washington Post and who has been singled out for criticism throughout his administration. It also included two friends of Mr. Trump — Micky Arison, a top executive at Carnival Cruises, and Phil Ruffin, a Las Vegas casino owner.