(CNN) Jeffrey Epstein, the multimillionaire accused of sexually abusing dozens of underage girls, appeared in public for the first time Wednesday since having been found last week in his jail cell with marks on his neck.

Attending a conference in his case in Manhattan federal court, Epstein showed no visible signs of injury as he learned from prosecutors that his trial on federal sex trafficking charges will likely take between four and six weeks next year.

US District Court Judge Richard Berman didn't set a tentative trial date, as prosecutors and defense counsel couldn't agree on whether the proceedings should be set for June 2020, as prosecutors requested, or September 2020, as Epstein's lawyers wanted.

Assistant US Attorney Alison Moe told the court that there is a "public interest in bringing this case to trial as swiftly as manageable."

Epstein is charged with one count of sex trafficking of minors and one count of conspiracy to engage in sex trafficking. Prosecutors have accused him of operating a sex trafficking ring in which he both paid underage girls to have sex with them and paid some of them to recruit other victims.

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