Trump spoke to reporters Wednesday as he departed the White House for a trip to Indianapolis to sell his tax plan.
Asked about private travel by Price and Treasury Secretary Steven Mnuchin's alleged misuse of government planes, Trump alternately disputed the details and said he didn't "know much about it".
Asked Wednesday whether he would fire Price, Trump said: "We'll see".
The chartered flights represent a "gross misuse" of public funding, the representatives said.
CBS46 political analyst Bill Nigut says the timing is not good for Price. Price made two brief appearances in Nashville before and after the lunch. Charter plane operators estimated that the 24 flights would have cost $300,000.
In numerous instances of private travel, commercial flights were available that would have fit within his required travel schedule and saved thousands of dollars.
Price's use of private flights stands in contrast to his immediate predecessors, Kathleen Sebelius and Sylvia Mathews Burwell, who would typically fly commercial. Press Secretary Sarah Huckabee Sanders added that the flights were "not White House-approved travel". He blistered Attorney General Jeff Sessions after Sessions recused himself from the Justice Department's Russian Federation elections investigation, a decision that Trump blamed for the later appointment of special counsel Robert S. Mueller III.
Trump is not the only one looking into Price's pricey travel. "He takes that very seriously and has taken it to heart".
"I don't think there will be any charter trips until this review is complete", Price said this week on Fox News. These trips were on our dime, and Price needlessly used an exorbitantly expensive mode of travel as he hopped from spot to spot, dining with family members and checking in on property he owns along the way.
Earlier Wednesday, the House Oversight Committee began its own inquiry into federal agency travel.
Similar letters from the committee were sent to 23 other agencies and the White House, the website reported. As HHS secretary, he has questioned whether the Medicaid health insurance program for low-income people delivers results that are worth the billions of dollars taxpayers spend for the coverage. After speaking at an event with Republican Senate Majority Leader Mitch McConnell in Tennessee, the Mnuchins toured Fort Knox and later watched the solar eclipse after traveling on government planes.
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