Asked if he was thinking about firing Price, the President was non-committal.
"We'll see," Mr. Trump added.
The President's remarks came as a key committee in Congress asked the White House for information on private charter jet flights taken by top Administration officials - and how much government money was being spent for those flights.
"The Committee is examining the extent to which non-career officials at federal departments and agencies either use government-owned aircraft for personal travel or private non-commercial aircraft for official travel," read a bipartisan letter sent to White House Chief of Staff.
Signed by Rep. Trey Gowdy (R-SC) and Rep. Elijah Cummings (D-MD), the letter is the clearest signal yet that Congress is raising red flags about private charter travel, detailed in recent stories about HHS Secretary Tom Price, EPA Administrator Scott Pruitt, and Treasury Secretary Steven Mnuchin.
Gowdy and Cummings - the top two members of the House Oversight Committee - asked for documents and information on such flights by October 10.
Last week, when stories first emerged about travel by Price on charter flights, officials at the Department of Health and Human Services defended his decision to take private jets instead of commercial flights.
"The travel department continues to check every possible source for travel needs including commercial, but commercial travel is not always feasible," the statement read.
But since then, there have been more stories which showed Price taking private jet flights to various meetings, mixed in with visits with family and friends.
The details have led to some rumblings about Price from within the Trump Administration.
Price not only faces this review by Congress, but also an investigation of his travel costs by the Inspector General at the Department of Health and Human Services.
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