President Trump and the writer E. Jean Carroll are arguing over whether a Supreme Court decision affording him substantial criminal immunity also shields him from having to pay tens of millions in damages for insulting her and saying she lied about his sexually assaulting her.

Mr. Trump made his arguments last year in his appeal of the $83.3 million verdict by a jury that found him liable for defaming Ms. Carroll in 2019 after she accused him of a decades-old attack. On Monday, Ms. Carroll pushed sharply back.

Her lawyer, Roberta A. Kaplan, argued in a brief that Mr. Trump’s view of the Supreme Court’s ruling, which protected him from charges that he tried to overturn the 2020 election, was too expansive. His statements calling Ms. Carroll’s accusation “a complete con job” and “a Hoax and a lie,” were strictly personal, she wrote. She said they fell far outside the boundaries of the official acts that presidential immunity protects.

“If there were ever a case where immunity does not shield a president’s speech, this one is it,” Ms. Kaplan said in her brief.

The dispute over the Supreme Court’s landmark decision, which addressed the scope of a president’s immunity from prosecution, comes as Mr. Trump has seen criminal cases against him in two states come to an end, and a third delayed indefinitely. In a fourth case, in New York, after Mr. Trump was found guilty of 34 counts in a trial stemming from a hush-money payment to a porn star, the judge imposed no jail time.

But Ms. Carroll’s legal battle with Mr. Trump — fought in two lawsuits spanning more than half a decade and now based in the federal appeals court for the Second Circuit in Manhattan — continues to move forward.

“Presidential immunity forecloses any liability here and requires the complete dismissal of all claims,” Mr. Trump’s lawyer, D. John Sauer, said in an appeals brief in September, citing the Supreme Court decision of last summer. (Mr. Trump has since chosen Mr. Sauer to serve in his administration as the U.S. solicitor general.)

Last month, the Second Circuit appeals court upheld a $5 million judgment against Mr. Trump in the other lawsuit that Ms. Carroll filed against him in Manhattan.

In that case, a federal jury in May 2023 found Mr. Trump liable for sexually abusing Ms. Carroll in a Bergdorf Goodman dressing room in the mid-1990s. It also found that he had defamed her when, in 2022, he said on Truth Social that her case was a hoax and a lie.

Ms. Carroll testified in the 2023 trial that she ran into Mr. Trump at the Fifth Avenue department store, and he asked for her help buying a present for a female friend. She said they ended up in the lingerie department, where Mr. Trump forced her into a dressing room and shoved her against a wall. He then pulled down her tights and inserted his finger and then his penis into her vagina, she testified.

Ms. Carroll had accused Mr. Trump of rape. The jury of six men and three women found that she had been sexually abused by Mr. Trump, but did not find he had raped her. The jurors have never said why they selected the lesser offense of sexual abuse over rape, which under New York law at the time was defined as sexual intercourse without consent that involves penetration of the penis in the vaginal opening.

The trial judge, Lewis A. Kaplan of U.S. District Court, ruled that Mr. Trump had waived any immunity argument when he did not raise it early in the litigation.

The $83.3 million jury verdict against Mr. Trump came in Ms. Carroll’s second trial, held in January 2024. That case stemmed from comments Mr. Trump made in 2019, when he was still in office during his first term, after Ms. Carroll first accused him, in a New York magazine book excerpt, of raping her in the dressing room.

Mr. Trump called her allegation false and said he had never met Ms. Carroll and did not know who she was. He continued to attack her in social media posts and at news conferences.

Ms. Carroll kept the assault a secret for years, telling only two close friends, before she disclosed it in the magazine excerpt.