President Trump’s pick to lead the Department of Veterans Affairs, David J. Shulkin, vowed at his Senate confirmation hearing Wednesday to reform — but not privatize — veterans’ health care, potentially putting him at odds with Mr. Trump’s campaign promise to allow all veterans to choose private health care.

“V.A. is a unique national resource that is worth saving,” Dr. Shulkin told the Senate Veterans Affairs Committee. He added, “The Department of Veterans Affairs will not be privatized under my watch.”

Dr. Shulkin, who is currently the department’s under secretary of health, was nominated as secretary of veterans affairs after a number of other candidates reportedly turned down Mr. Trump’s overtures. Before taking his current position in 2015, Dr. Shulkin helped lead several private health care systems, including Beth Israel Medical Center in New York and the University of Pennsylvania Health System.

Veterans groups and members of Congress have credited him with making real, if ponderous, progress in improving care in the veterans’ vast health system, which includes 1,234 clinics and hospitals. In his 18 months heading the system, Dr. Shulkin oversaw the hiring of more than 10,000 doctors and nurses, and authorized more than three million appointments with private providers.