“So she calls me up: ‘It’s the nicest thing that’s ever happened; thank you so much,’” Mr. Trump said at the rally, mocking the congresswoman’s voice while recounting their call. He suggested that Ms. Dingell had begged for him to lower American flags to half-staff and, apparently impersonating her, said: “Do this, do that, do that. Rotunda.”

Mr. Dingell did not lie in state in the Capitol Rotunda — Ms. Dingell said on Thursday that that had not been one of his requests. Still, Mr. Trump said Ms. Dingell had said her husband would be thrilled as he looked down and saw how the country was honoring him.

“Maybe he’s looking up,” Mr. Trump said at one point. “I don’t know. I don’t know, maybe. Maybe. But let’s assume he’s looking down.”

Ms. Dingell said the president had ordered American flags lowered, but beyond that, Mr. Dingell’s military service in World War II made him eligible for the only request he had made, which was to be buried at Arlington National Ceremony. At the time, she said, she had welcomed the president’s call — emphasizing that he called her.

“He was very kind,” Ms. Dingell said. “He had told me that he heard he was a great man and I thought it was very thoughtful for him to call at a time when I was really grieving.”

But Mr. Trump’s public remarks about their exchange were condemned by both Republicans — including Representative Fred Upton, who faces re-election next year in Michigan — and Democrats, including former Vice President Joseph R. Biden Jr., a leading 2020 candidate whose own political life has been punctuated by loss.

“This is equally as cruel as it is pathetic,” Mr. Biden, whose son Beau died in 2015, said on Twitter, “and it is beyond unconscionable that our President would behave this way.”