Standing at his final rally of the 2024 campaign, former President Donald J. Trump in the first minutes after midnight on Election Day used a crude sexist remark to attack Representative Nancy Pelosi, the former House speaker who is one of his longstanding political rivals.

“She’s a bad person,” Mr. Trump said at the Van Andel Arena in Grand Rapids, Mich. “Evil. She’s an evil, sick, crazy —” He made an exaggerated face, his mouth open wide to draw attention to the next syllable: “Bi—”

Then he held up a finger dramatically, feigning that he’d caught himself. “Oh no,” he said. As the crowd of thousands began laughing, Mr. Trump mouthed the word into the microphone. “It starts with a B, but I won’t say it,” Mr. Trump added. “I want to say it.”

As the crowd roared even louder, some of the attendees began to supply the word he’d barely omitted, shouting, “Bitch!”

In the closing days of the race, Mr. Trump has made direct appeals to women as he stares down a gender gap in the polls that has concerned him and his team. He has tamped down mentioning his role in appointing Supreme Court justices who overturned the constitutional right to an abortion, an issue that polls show to be a top concern to female voters.

Yet at the same time, Mr. Trump has used misogynistic language to refer to Vice President Kamala Harris and has fostered an environment at his rallies where speakers and attendees feel comfortable making the kind of gendered insults that, in another political era, would have been unthinkable to say in public.