According to an indictment, Mr Epstein arranged for girls under the age of 18 to perform nude "massages" and other sex acts for him in his NY and Florida homes, and paid some girls to recruit others, from at least 2002 to 2005.
Authorities said in a press conference that nude photographs of underage girls were found in Epstein's NY mansion, with one prosecutor saying "the alleged behavior shocks the conscience".
A hearing on Epstein's bail request is scheduled for early July 15.
Acosta, who approved the earlier deal, announced Friday he was stepping down as labor secretary amid the controversy.
Trump didn't just praise Acosta's character and his heritage; he also defended him against scrutiny for his role in Epstein's deal. He added that he didn't think it was right for his handling of Epstein's case to distract from his work as secretary of labour.
U.S. District Judge Richard Berman said Friday that Epstein's lawyers can file documents related to his finances under seal, keeping them out of the public docket.
Secretary of Labor Alexander Acosta's resignation announcement on Friday sparked demands from progressive groups for Congress to "hold abusers and their enablers"-including President Donald Trump-"accountable".
In 2015, Epstein's address book was published online by news outlet Gawker, which obtained the book following its appearance in court proceedings after Epstein's former house manager tried to sell it in 2009.
New York-born Epstein worked as a teacher before moving into finance. Prosecutors have urged other alleged victims to come forward, and they are likely looking to identify those underage girls seen in a trove of pornography taken from Epstein's Manhattan mansion.
"While NBC's Stephanie Gosk gave a passing mention to both Clinton and Trump (without any mention of the "Lolita Express"), CBS This Morning's Mola Lenghi spent more time on both Trump and Clinton, while emphasizing comments Trump made praising Epstein in 2002".
The indictment alleges Epstein "enticed and recruited" underage girls to his properties in Manhattan and in Palm Beach, Fla. "I have done many [cases] much less troubling than this one where [prosecutors] would never make a downward argument like this".
It allowed Epstein to avoid federal charges, and instead serve 13 months in jail after pleading guilty to state charges including solicitation of prostitution (including one charge involving a minor under the age of 18).