Lawyers for Jeffrey Epstein’s convicted co-conspirator, Ghislaine Maxwell, said in a letter to Congress on Monday that she was unwilling to testify without a grant of immunity or presidential action to shorten her 20-year prison sentence.

Public attention has shifted recently to the prospect of Ms. Maxwell’s testimony to lawmakers after the Trump administration suddenly reversed course and refused to release any more evidence from the Epstein investigation.

Jeffrey Epstein, a well-connected multimillionaire, hung himself in a federal prison cell in 2019 shortly after he was arrested and charged with sex trafficking. An investigation more than a decade earlier ended in Mr. Epstein pleading guilty to state charges in Florida that resulted in an unusually light sentence for the crime of paying underage girls to perform sex acts.

After Mr. Epstein’s death, Ms. Maxwell was charged and convicted of conspiring to recruit female minors who were sexually abused by Mr. Epstein, but the case has generated a host of suspicions and accusations about others. For months, Attorney General Pam Bondi and other senior Trump officials publicly teased the pending release of important new details about the Epstein investigation, only to sharply reverse course this month and insist no more information would be provided, angering many of their own supporters.

Mr. Trump was a longtime friend of Mr. Epstein before the two had a falling out in 2004. The president has denied any wrongdoing and expressed exasperation in recent days that he is still fielding questions about the case.

Last week, The New York Times and The Wall Street Journal reported that Ms. Bondi informed Mr. Trump in the spring that his name appeared in the Epstein files, although it wasn’t clear in what context, and F.B.I. files are often a mix of relevant evidence, unverified claims, and nonincriminating information.