Fighting to keep his job, US Health Secretary Tom Price has said he will write a personal check to reimburse taxpayers for his travel on charter flights taken on government business and pledged to fly commercial in future with “no exceptions.”

The repayment — $51,887.31, according to Mr Price's office — covered only the secretary's seat. Mr Price did not address the overall cost of the flights, which could reportedly amount to more than $400,000 and is under investigation.

“I regret the concerns this has raised regarding the use of taxpayer dollars,” Mr Price said. “I was not sensitive enough to my concern for the taxpayer.” His mea culpa came a day after a public rebuke from President Donald Trump.

A former congressman from Georgia regarded as a conservative policy expert, Mr Price said he hopes to keep his Cabinet seat. At the White House, press secretary Sarah Huckabee Sanders would not go that far.

“We're going to conduct a full review and we'll see what happens,” Ms Sanders said.

Mr Price said the president had personally let him know of his displeasure. “As he has said publicly, he wasn't happy, and he expressed that to me very clearly,” Mr Price said told Fox News.

All his travel was legally approved by officials at Health and Human Services, Mr Price said. It amounted to 10 trips with 26 different segments.

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On Wednesday, Mr Trump had declared that he's “not happy” over reports that Mr Price flew on costly charters when he could have taken cheaper commercial flights. Asked whether he'd fire Mr Price, the president said, “We'll see.”

Mr Price later said: “I think we've still got the confidence of the president.” About the controversy, he said, “We're going to work through this.”

Taxpayers “won't pay a dime for my seat on those planes,” Mr Price said in his statement.

Mr Price played a supporting role in the fruitless Republican effort to repeal Barack Obama's health care law — another source of frustration for the president.

Bernie Sanders grills Tom Price on Trump's health care plans

Prompted partly by controversy over Price, the House Oversight and Government Reform Committee has launched a wide-ranging investigation into travel by Mr Trump's political appointees. On Wednesday the committee sent requests for detailed travel records to the White House and 24 departments and agencies, dating back to the president's first day in office.

Trips by Treasury Secretary Steven Mnuchin and Environmental protectection Agency Administrator Scott Pruitt have also drawn criticism.

A senior Republican senator urged Mr Trump to lay down some rules. “Considering the many travel options to and from Washington, DC, I'm urging you to emphasise to cabinet secretaries the necessity of using reasonable and cost-effective modes of travel in accordance with federal restrictions,” Sen. Chuck Grassley, R-Iowa, wrote in a letter to the president.

Mr Price's travels were first reported last week by Politico, which said cheaper commercial flights were a viable option in many cases.

On a June trip to Nashville, Mr Price also had lunch with his son, who lives in that city, according to Politico. Another trip was from Dulles International Airport in the Washington suburbs to Philadelphia International Airport, a distance of 135 miles.

Last Friday the Department of Health and Human Services (HHS ) inspector general's office announced it was conducting a review to see if Mr Price complied with federal travel regulations, which generally require officials to minimise costs.

Mr Price's office had initially said the secretary's demanding schedule sometimes did not permit the use of commercial airline flights. Mr Price says he's fully cooperating with investigators.

Mr Price, an ally of House Speaker Paul Ryan, is a past chairman of the House Budget Committee, where he was a frequent critic of wasteful spending. 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. He's a former orthopedic surgeon who once practiced in an inner-city hospital.