WASHINGTON >> A day after President Donald Trump’s rebuke, health secretary Tom Price promised today to reimburse taxpayers for his cost on charter flights taken while on government business. He issued a public apology as he fought to keep his job.

“I regret the concerns this has raised regarding the use of taxpayer dollars,” Price said in a statement. “I was not sensitive enough to my concern for the taxpayer.”

The Health and Human Services secretary said he’ll swear off charter flights — “no exceptions” — and repeated his promise to fully cooperate with ongoing investigations.

Price also said he hopes to keep his job, but at the White House, press secretary Sarah Huckabee Sanders wouldn’t go that far.

“We’re going to conduct a full review and we’ll see what happens,” Sanders told reporters.

On Wednesday Trump declared that he’s “not happy” with his health chief over reports that Price flew on costly charters when he could have taken cheaper commercial flights on government business. Asked whether he would fire Price, Trump said, “We’ll see.”

Price told reporters today, “I think we’ve still got the confidence of the president.” About the controversy, he said, “We’re going to work through this.”

In his statement, Price said he would write a personal check today covering his travel costs on charter flights. “The taxpayers won’t pay a dime for my seat on those planes.” He did not address the costs incurred by those traveling with him.

His office did not respond when asked how much Price would pay. It’s unclear if it would cover the full difference for flying the secretary’s entourage on charters as compared to commercial airlines.

A former GOP congressman from Georgia, Price also played a supporting role in the fruitless Republican effort to repeal Barack Obama’s health care law — another source of frustration for the president.

Prompted partly by controversy over Price, the House Oversight and Government Reform Committee launched a wide-ranging investigation into travel by 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.

The letters were signed by the committee’s chairman, Rep. Trey Gowdy, R-S.C., and its ranking Democrat, Elijah Cummings of Maryland. Lawmakers are demanding information on use of government planes for personal travel, as well as use of private charters for official travel. The committee wants details by Oct. 10.

The president vented his displeasure with Price to reporters on Wednesday as he left the White House for a trip to sell his tax overhaul in Indianapolis.

“I was looking into it, and I will look into it, and I will tell you personally I’m not happy about it,” Trump responded when asked about Price’s travel. “I am not happy about it. I’m going to look at it. I’m not happy about it and I let him know it.”

Price’s travels were first reported last week by Politico, which said it had identified a couple dozen charter flights at a cost of hundreds of thousands of dollars. Cheaper commercial flights were a viable option in many cases.

On a June trip to Nashville, 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 HHS inspector general’s office announced it was conducting a review to see if Price complied with federal travel regulations, which generally require officials to minimize costs.

Price’s office had initially said the secretary’s demanding schedule sometimes did not permit the use of commercial airline flights.

Trump’s publicly expressed displeasure — or ambivalence — has been a sign in the past that the tenure of a key aide will soon be over.

In August, the president was asked if he still had confidence in Steve Bannon, then a senior strategist in the White House. “He’s a good person. He actually gets very unfair press in that regard. But we’ll see what happens with Mr. Bannon,” Trump said. Bannon was out three days later.

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.