Top Democrats are calling for the resignation of President Donald Trump's labor secretary, Alex Acosta, over his handling of the case against wealthy financier and accused sex trafficker Jeffrey Epstein more than a decade ago.

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In a series of statements posted Tuesday on Twitter, Acosta said he was "pleased that NY prosecutors are moving forward with a case based on new evidence."

"With the evidence available more than a decade ago, federal prosecutors insisted that Epstein go to jail, register as a sex offender and put the world on notice that he was a sexual predator," he wrote. "Now that new evidence and additional testimony is available, the NY prosecution offers an important opportunity to more fully bring him to justice."

Acosta was the U.S. attorney in Florida when Epstein cut a secret deal to avoid significant jail time and federal prosecution after he was accused of molesting dozens of teenage girls. Epstein had faced sex trafficking charges but pleaded guilty instead to a pair of lesser charges in 2008.

House Speaker Nancy Pelosi called for Acosta to step down in a statement posted late Monday to Twitter, calling the deal made with Epstein "unconscionable."

While speaking on the Senate floor Tuesday, Senate Minority Leader Chuck Schumer said Acosta cut a "sweetheart deal" with Epstein "despite overwhelming evidence."

"I am calling on Secretary Acosta to resign. It is now impossible for anyone to have confidence in Secretary Acosta's ability to lead the Deptartment of Labor," Schumer said.

"Instead of prosecuting a predator and serial sex trafficker of children, Acosta chose to let him off easy. This is not acceptable. We cannot have, as one of the leading appointed officials in America, someone who has done this. Plain and simple."

Trump told reporters Tuesday that his administration would be looking "very carefully" at how Acosta handled the 2008 case. However, he emphasized that "if you go back and look at everybody else's decisions – whether it's a U.S. attorney or an assistant U.S. attorney or a judge – you go back 12 or 15 years ago, or 20 years ago, and look at their past decisions, I would think you'd probably find that they would wish they maybe did it a different way."

The deal made between prosecutors and Epstein in 2008, in which he was required to serve 13 months in jail, was kept secret from his victims so they would not object, according to the Miami Herald. The newspaper examined the deal in a series of in-depth reports published last year.

U.S. District Judge Kenneth Marra, of Florida, determined in February that the deal violated the Crime Victims' Rights Act, as Epstein's victims should have been consulted before the deal was struck, according to The Daily Beast and The Associated Press.

Authorities arrested Epstein on Saturday to face new charges of sex trafficking and sex trafficking conspiracy. Federal prosecutors in New York's Southern District accused him of sexually exploiting and abusing dozens of girls, some as young as 14, between 2002 and 2005 in New York and Florida.

The Associated Press contributed to this report.