Asked if Price would be fired, Trump left the option open.
"We'll see," he said. "I'm looking at that very closely. I am not happy with him."
Price, for his part, has defended the travel as work related while a housing department spokeswoman has insisted the secretary flies commercial when possible. The HHS inspector general's office says it is reviewing the private flights.
President Trump on HHS Secretary Tom Price's private jet controversy: "I am not happy about it and I let him know it" pic.twitter.com/7SZaSEouTo
But Trump insisted that Republicans "have the votes" to make good on a longtime promise to repeal and replace Obamacare, reasoning that the latest health care effort stalled because of one unnamed senator who Trump said was in the hospital.
It is unclear which senator Trump was referring to; Sen. Thad Cochran, R-Mississippi, has been ill but is not actually in the hospital.
The president predicted a health care vote early next year, but said he planned to work in a bipartisan fashion on the issue going forward.
But until then, Trump previewed an executive order to achieve one of the few health care specifics he'd campaigned on: buying health care coverage across state lines. That order, Trump said, would be signed "probably" next week."
Trump also continued his crusade against NFL players who kneel during the national anthem, denying that he was contradicting the First Amendment as he urged the league to fire players who protest.
The NFL, the president said, is in a "very bad box" and again stated that players "cannot [kneel] during the national anthem."
The NFL has "to change or their business is going to go hell," he maintained.
Trump also spoke about the Alabama senate GOP run-off on Tuesday that saw his preferred candidate defeated at the hands of a more controversial option.
Luther Strange, the incumbent who earned Trump's backing, "came a long way," the president said, but the runoff's winner, Roy Moore, now had the president's support. Moore, Trump said, is "going to be a great senator." The election is in December.