WASHINGTON—Health and Human Services Secretary Tom Price said he would stop traveling on private jets and reimburse the federal government more than $50,000 for his flights, a day after President Donald Trump said he wasn’t pleased with the practice and signaled it could endanger his job.

“I will take no more private charter flights as secretary of HHS,” Dr. Price said in a statement on Thursday. “No exceptions.”

Dr. Price, a former Republican congressman from Georgia, said he would fully cooperate with the previously disclosed inspector general’s investigation into his travel. He added that he has launched another internal HHS review on the matter.

On Wednesday, Mr. Trump told reporters he was “not happy” with Dr. Price over his use of private jets. Asked whether he planned to fire Dr. Price over the flap, the president said, “We’ll see.”

Dr. Price said he would write a personal check to the U.S. Treasury to reimburse the government “for the expenses of my travel on private charter planes.” He reiterated that all of this travel was approved by legal and HHS officials. “Despite this, I regret the concerns this has raised about the use of taxpayer dollars,” he said.