“So in other words, when you sign up when you go into the military, you are really signing up to die,” she said of the president’s comments. “That is not what you say to a grieving widow, a woman who just learned that her husband cannot have an open casket funeral. In fact, she will probably not even be able to see his body.”

Ms. Wilson said she became “livid” at Mr. Trump’s comments, and motioned to the military officials in the limousine that she wanted to speak with the president herself. But she said they would not allow it.

Instead, the conversation continued for several more minutes with Ms. Wilson crying.

“When she got off the phone, she said, ‘He didn’t even know his name. He kept calling him, ‘Your guy,’ ” Ms. Wilson recalled the widow saying. “He was calling the fallen soldier, ‘your guy.’ And he never said his name because he did not know his name. So he kept saying, ‘Your guy. Your guy. Your guy.’ And that was devastating to her.”

At the White House on Wednesday, Sarah Huckabee Sanders, Mr. Trump’s press secretary, defended the president’s comments. “Just because the president said ‘your guy,’ I don’t think that means he doesn’t know his name,” Ms. Sanders said.