“I had a doctor that gave me a letter — a very strong letter on the heels,” Mr. Trump said in the interview.

Asked to provide The Times with a copy of the letter, which he had obtained after his fourth student deferment, Mr. Trump said he would have to look for it. A spokeswoman later did not respond to repeated requests for copies of it.

The Selective Service records that remain in the National Archives — many have been discarded — do not specify what medical condition exempted Mr. Trump from military service.

Mr. Trump has described the condition as heel spurs, which are protrusions caused by calcium built up on the heel bone, treated through stretching, orthotics or sometimes surgery.

Mr. Trump said that he could not recall exactly when he was no longer bothered by the spurs, but that he had not had an operation for the problem.

“Over a period of time, it healed up,” he said.