President-elect Donald J. Trump on Monday failed to overturn a $5 million judgment that he sexually abused the writer E. Jean Carroll in a Bergdorf Goodman dressing room in the mid-1990s and later defamed her.

Mr. Trump’s lawyers argued to a federal appeals panel that a lower court in Manhattan had erred by allowing two women to testify in the Carroll trial that he had also sexually assaulted them. The lawyers also argued that the court should not have allowed Ms. Carroll’s lawyers to play the recording of the “Access Hollywood” conversation in which Mr. Trump bragged in vulgar terms about grabbing women by the genitals.

The appeals court rejected Mr. Trump’s request for a new trial in the case, which produced the smaller of two defamation judgments against him. “Mr. Trump has not demonstrated that the district court erred in any of the challenged rulings,” the opinion by the U.S. Court of Appeals for the Second Circuit said. It was unsigned but issued by a panel that included the judges Denny Chin and Susan Carney — appointed by President Barack Obama — as well as Myrna Perez, appointed by President Biden.

“Both E. Jean Carroll and I are gratified by today’s decision,” Roberta Kaplan, Ms. Carroll’s lawyer, said in a statement. “We thank the Second Circuit for its careful consideration of the parties’ arguments.”

Steven Cheung, Mr. Trump’s chief campaign spokesman, who is set to be his White House communications director, said Mr. Trump was re-elected with an “overwhelming mandate,” and he said the American people “demand an immediate end to the political weaponization of our justice system and a swift dismissal of all of the witch hunts, including the Democrat-funded Carroll hoax, which will continue to be appealed.”

Mr. Trump was represented in the appeal by D. John Sauer, his pick for U.S. solicitor general. The ruling came as Mr. Trump prepares to take the presidency next month amid unceasing legal entanglements. This month, he accused a juror of misconduct that he said should void a 34-count felony conviction in Manhattan. He also sued The Des Moines Register for running a poll that showed him trailing Vice President Kamala Harris. ABC News this month settled a defamation lawsuit brought by Mr. Trump, agreeing to pay $15 million.

During the trial last year, Ms. Carroll testified that she had run into Mr. Trump at Bergdorf’s on Fifth Avenue and he asked her to help him buy a present for a female friend. Ms. Carroll testified that they wound up in the lingerie department, where he pulled her into a dressing room, shut the door and began assaulting her.

Ms. Carroll said he shoved her against a wall, pulled down her tights and inserted his fingers and then his penis into her vagina. She said she pushed him away and fled. Other than telling two friends, she kept the encounter secret until disclosing it in a 2019 book excerpt in New York magazine.

Mr. Trump did not testify at the trial but denied wrongdoing and claimed he had never met Ms. Carroll. He earned a rebuke from the judge, Lewis A. Kaplan, when he posted on Truth Social that Ms. Carroll’s lawsuit was a scam and wrote that Ms. Carroll’s lawyer was a “political operative.” He also said that the dress Ms. Carroll wore at Bergdorf’s that day should be “allowed to be part of the case.”

The jury of six men and three women found that Mr. Trump had sexually abused Ms. Carroll but did not find that he raped her. It was unclear why jurors chose the lesser offense of abuse over rape, which is defined under state law as sexual intercourse without consent that involves any penetration of the penis in the vaginal opening.

The federal jury also found that Mr. Trump defamed Ms. Carroll when he wrote on Truth Social in 2022 that her case was a “a complete con job” and “a Hoax and a lie.” The jury ordered him to pay Ms. Carroll $5 million in damages.

This year, another Manhattan jury ordered Mr. Trump to pay Ms. Carroll $83.3 million for defaming her in 2019 after she accused him of rape, and continuing to do so in social media posts at news conferences and even during the trial. Ms. Carroll’s lawyers argued that a large award was necessary to stop Mr. Trump from continuing to deride her.

Mr. Trump as recently as last week shared a post from another user on Truth Social that contained an image that read: “Should a woman go to jail for falsely accusing a man for rape?” above photos of Ms. Carroll and Mr. Trump. The post encouraged others to share the post “if you want justice for Trump.”