WASHINGTON (BLOOMBERG) - President Donald Trump said he was looking "very closely" at whether to dismiss embattled Health and Human Services (HHS) Secretary Tom Price, whose travel is at the centre of a widening uproar over taxpayer-funded flights by top administration officials.

Price is facing two investigations into his use of private jets. Asked by reporters on Wednesday (Sept 27) whether he would fire the health secretary, Trump said "we'll see." "I am not happy with him," the president said.

The White House won't defend Price's use of charter flights for routine travel, an official said, calling it an inappropriate use of federal money.

Trump is also displeased with Price over the failure so far to pass legislation repealing and replacing Obamacare, but has kept him on because of Price's relationship with House Speaker Paul Ryan, according to a person close to the president.

Earlier in the day, 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."

The letter, signed by the committee's top Republican and Democrat, gives Price two weeks to provide the records. It also drags the former congressman into an inquiry led by fellow Republicans, a relative rarity in Washington politics.

HHS said that it has initiated its own review of travel processes and procedures and will fully cooperate with Congress and the agency's Office of Inspector General, which is also investigating Price's trips.

The oversight letter is part of a wider probe by the committee into the use of government planes or private aircraft by senior Trump administration officials. Treasury Secretary Steven Mnuchin was criticised after he and his wife took an Air Force jet on Aug 21 to meet with business leaders in Kentucky and visit the Fort Knox gold reserves.

Mnuchin and his staff also requested a government plane for his honeymoon in August, though he didn't use the jet. Environmental Protection Agency head Scott Pruitt also flew on private planes several times, CBS News has reported.

Price is a particular focus after reports by Politico that he took at least two dozen charter flights costing hundreds of thousands of dollars, despite the availability of cheaper commercial tickets.

He also paired official trips with visits to longtime colleagues and family members, including his son, a musician in Nashville, Politico reported.

Price took over the HHS job in February, and part of his role has been to push for repeal of the Affordable Care Act. Those efforts have failed so far, with Senate Republicans dropping their latest effort to overturn former President Barack Obama's marquee law earlier this week.

White House press secretary Sarah Huckabee Sanders said on Monday that Price's travel wasn't approved by the White House, but that there were likely "certain instances" when private charter travel would be appropriate. In the meantime, jet use has been suspended, Sanders said.

Last week, Price spokesman Charmaine Yoest defended the secretary's travel. "The travel department continues to check every possible source for travel needs including commercial, but commercial travel is not always feasible," she said.

Representative Trey Gowdy, the South Carolina Republican who chairs the oversight committee, declined to comment on whether Price should stay in the job.

"It was not my job to give President Obama hiring or firing advice nor is it my job to give President Trump hiring or firing advice," Gowdy said in an emailed statement. "Our job is to accumulate facts to elucidate the truth."

Democrats have pounced on the jet trips. Five House Democrats sent a letter to Price on Wednesday calling on him "to do the right thing and immediately tender your resignation." Representative Frank Pallone, the top Democrat on the House Energy and Commerce Committee, said that if the allegations against Price are true, Price "should reimburse taxpayers for the funds he spent on private jets and apologise to the American people for his gross breach of the public trust."

Pallone also said he was shocked by "the outright hypocrisy of these actions from a man who has spent his career railing against government waste."

In 2009, Price told CNBC that Congress should cut spending on government planes that supporters said were needed to carry military officials leading soldiers into combat. Price criticised an original effort to spend US$550 million (S$744 million) on eight passenger jets, and also objected to a reduced $220 million request for four jets.

"Now we need to cut it from four jets to zero jets," he said at the time. "This is just another example of fiscal irresponsibility run amok in congress right now."

Former Health and Human Services Secretary Kathleen Sebelius called Price's use of chartered aircraft "stunning," in a meeting Tuesday with Bloomberg reporters and editors.

During her tenure, Sebelius said, health department officials were required to fly economy class for all travel less than 12 consecutive hours. Her lone charter flight, she said, was in a propeller plane her staff hired to visit three Alaskan villages inaccessible by road or commercial aircraft.