Asked if he had confidence in Price after the reports on his travel, Trump said: "I am looking at that very closely.
And I will tell you personally, I'm not happy about it", Trump told pool reporters Wednesday afternoon when asked if he would dismiss the former Georgia congressman.
Price is not the only member of the Cabinet to be in a precarious position with Trump.
During a wild and widely panned speech at the Boy Scout Jamboree in July, President Donald Trump famously threatened, tongue in cheek, to fire Tom Price if he did not help get Obamacare repealed and replaced.
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However, he has proven to be more moderate in his previous stints in government than his rhetoric while in opposition suggests. Prime Minister Bill English's National Party won 46 percent of the vote, according to the electoral commission on Sunday.
Tesia D Williams, a spokeswoman for the HHS inspector general, told the BBC the agency is reviewing whether it was "potentially inappropriate travel".
On Wednesday, the House Committee on Oversight and Government Reform released a letter asking Price for details on his use of "government-owned aircraft for personal travel or private non-commercial aircraft for official travel".
Federal regulations stipulate that "official travel on the part of federal employees must be "by the most expeditious means of transportation practicable" and 'commensurate with the nature and objective of the [employee's] duties, ' and by no means should include personal use", according to the letter. The flight to Nashville cost more than $17,700.
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Price has taken at least two dozen private charter flights since May at a cost to taxpayers of about $300,000, according to Politico, which first reported the travel.
According to a former Obama administration official who is in close touch multiple Health and Human Services officials in the building, there has been growing frustration with each new report of Price's private charter plane use.
HHS' Assistant Secretary for Public Affairs Charmaine Yoest said that the chartered flights were booked due to Price's "incredibly demanding" schedule, and that the department looks at all possibilities for travel before booking accommodations. Mnuchin also viewed the solar eclipse from Kentucky, a prime viewing spot, the same day. Cheaper commercial flights were a viable option in many cases.
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She paced back and forth outside the exclusive Melrose Avenue store, shouting and waving the machete. Investigators are examining security video of the incidents in an effort to identify the woman.