ERIE, Pa. — Senator Tim Kaine of Virginia, Hillary Clinton’s running mate, challenged Donald J. Trump on Tuesday to be more forthcoming about his health, taking aim at Mr. Trump over an issue he has tried to use to undermine Mrs. Clinton.

As part of a lengthy critique of Mr. Trump, Mr. Kaine mocked a four-paragraph letter signed last year by a doctor for Mr. Trump, which proclaimed the candidate’s strength and stamina to be “extraordinary” and declared that he would be “the healthiest individual ever elected to the presidency.”

The doctor, Harold N. Bornstein, told NBC News last week that he had written the letter in five minutes while a black car waited outside his office to collect it. As for his choice of words about Mr. Trump, Dr. Bornstein said he “picked up his kind of language and then just interpreted it to my own.”

Mr. Trump “won’t even release credible information about his health,” Mr. Kaine said at a waterfront rally, where the picturesque backdrop included a paddle-wheel boat with the initials V.P. (for Victorian Princess, not vice president).