E. Jean Carroll, who this month won $5 million in damages from former President Donald J. Trump, is now seeking a “very substantial” additional amount in response to his insults on a CNN program just a day after she won her sexual abuse and defamation case.

Ms. Carroll’s filing Monday in Manhattan federal court seeks to intensify the financial pain for Mr. Trump. The jury in her civil case found him liable on May 9 for sexual abuse and defamation. It ordered him to pay Ms. Carroll, a former advice columnist and fixture in Manhattan’s media circles, $2 million for the sexual abuse and $3 million for the defamation.

Monday’s filing came in a separate defamation lawsuit that Ms. Carroll had filed in 2019 against Mr. Trump, 76, which is before the same judge who presided in the civil trial. The older case stemmed from comments Mr. Trump made that year, shortly after she said that he had raped her in a Manhattan department store dressing room in the mid-1990s. That lawsuit had been sidetracked by appeals, but is still pending.

In a separate letter to the judge, Ms. Carroll’s lawyer, Roberta A. Kaplan, revealed with little elaboration that Mr. Trump has threatened to file a lawsuit against Ms. Carroll “in retaliation and possibly to seek sanctions.”

On May 10, Mr. Trump, who is seeking to regain the presidency, went on CNN and echoed his earlier denials about the episode, calling her account “fake” and a “made-up story.” Despite a photograph showing them together, he claimed again that he had never met Ms. Carroll, 79, called her a “wack job” and said the recent civil trial was “a rigged deal.”

The court filing on Monday argues Mr. Trump’s defamatory statements following the May 9 verdict “show the depth of his malice toward Carroll, since it is hard to imagine defamatory conduct that could possibly be more motivated by hatred, ill will or spite.”

“This conduct supports a very substantial punitive damages award in Carroll’s favor both to punish Trump, to deter him from engaging in further defamation, and to deter others from doing the same,” the filing says.

Mr. Trump continues to fight the jury’s decision. After the verdict, his lawyer Joseph Tacopina filed a notice of appeal.

Ms. Carroll’s lawyer, Ms. Kaplan, said in a brief interview Monday that Mr. Trump’s statements on CNN — “literally the day after the verdict” — made it all the more important for Ms. Carroll to pursue the pending defamation lawsuit.

“It makes a mockery of the jury verdict and our justice system if he can just keep on repeating the same defamatory statements over and over again,” Ms. Kaplan said.

She declined to comment on the reference in her letter to Mr. Trump’s threat of a lawsuit against Ms. Carroll.

In an extensive interview two days after the verdict, Ms. Carroll said of Mr. Trump’s CNN comments: “It’s just stupid; it’s just disgusting, vile, foul; it wounds people.” She added that she had been “insulted by better people.”

Her filing on Monday asks the judge, Lewis A. Kaplan of Federal District Court, to let her revise her 2019 defamation lawsuit to include the fact of the jury’s verdict against Mr. Trump as well as his statements on CNN and others he made about Ms. Carroll on his Truth Social platform.

Ms. Carroll has said that after Mr. Trump raped her in the dressing room at the Bergdorf Goodman department store, she kept the encounter a secret, other than confiding in two close friends, for more than 20 years. Ms. Carroll first disclosed the episode in a 2019 book excerpt in New York magazine.

At the time, Mr. Trump vehemently denied Ms. Carroll’s allegation, calling it “totally false” and saying he could not have raped her because she was not his “type.”