The suit is seeking to make the details of Epstein's secret plea deal public.
Mr Acosta himself weighed in on Twitter, ignoring the calls for his resignation and crediting the charges brought against Mr Epstein in NY to new evidence that "offers an important opportunity to more fully bring him to justice".
Acosta tweeted Tuesday amid growing calls from congressional Democrats for his resignation.
In a almost hour-long news conference, Acosta retraced the steps that federal prosecutors took in the case when he was USA attorney for the Southern District of Florida a decade ago, insisting that "in our heart we were trying to do the right thing for these victims". He pleaded not guilty on Monday.
However, the plea bargain "was not a bad deal" for the prosecution in the case, Dershowitz said.
He said prosecutors were working to avoid a more lenient arrangement that would have allowed Epstein to "walk free". The official could not discuss the matter publicly and spoke to AP on condition of anonymity. He and Acosta had both done work with the law firm Kirkland & Ellis.
That deal Epstein secretly cut allowed him to avoid federal prosecution for almost identical allegations. One of those parties was one Epstein threw for Prince Andrew, Duke of York, who's also been accused of and vehemently denies sexually abusing minors.
Jeffrey Epstein is challenging victims of his underage sexual abuse in a Florida court, hours after he was indicted on sex trafficking charges in a separate case.
Epstein had previously evaded similar charges when he secured a nonprosecution deal with federal prosecutors in Miami more than a decade ago. A West Palm Beach judge found this year that the deal had violated the Crime Victims' Rights Act because the victims were not informed or consulted. He could get up to 45 years in prison if convicted.
The women of the View discussed the Epstein drama on Tuesday, noting the men still at risk of getting implicated - including Presidents Bill Clinton and Donald Trump - and criticizing Labor Secretary Alex Acosta for the sweetheart deal he gave the billionaire more than a decade ago.
White House senior adviser Kellyanne Conway told reporters on Tuesday that Acosta was "doing a great job".
Brown isn't the first journalist to report on the allegations - investigative reporter Vicky Ward said earlier this week that Vanity Fair cut sexual misconduct allegations from a profile she wrote on Epstein in 2002.
Trump in 2002 told New York Magazine he'd known Epstein for 15 years, describing him as "a lot of fun to be with".
Dershowitz (left) was implicated in Epstein's alleged sex-trafficking scandal when one of the victims, Virginia Roberts Giuffre, alleged that she was held as a sex slave and loaned out to the famed attorney. "No doubt about it - Jeffrey enjoys his social life". "He knew about this when he nominated him for the Cabinet", she said.
Epstein has also won praise from former President Clinton for his philanthropic efforts, and Clinton frequently flew aboard Epstein's private jet.
Billionaire hedge fund manager Jeffrey Epstein was charged in a Manhattan federal court Monday with sex trafficking and conspiracy.
Sen. Ben Sasse, a Nebraska Republican who's a member of the Judiciary Committee, said at the time that he had received a letter from the Justice Department informing him that its Office of Professional Responsibility had "opened an investigation into allegations that Department attorneys may have committed professional misconduct" in their handling of the plea deal reached between Acosta, then the United States attorney in Miami, and Epstein.