WASHINGTON—Labor Secretary Alexander Acosta defended his handling of a case involving a financier accused of exploiting underage girls, in the face of calls from top Democrats that he resign since he oversaw the matter while he was a federal prosecutor.

Mr. Acosta struck a plea deal with financier Jeffrey Epstein in 2008, when he was the U.S. attorney in Miami, that has come under scrutiny because it ended with a federal nonprosecution agreement that critics said was too lenient.

This week, federal prosecutors in New York charged Mr. Epstein with two counts related to sex trafficking of minors. Mr. Epstein pleaded not guilty, and his defense team said prosecutors are improperly seeking a redo of the earlier investigation.

On Twitter, Mr. Acosta said Tuesday: “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 said he supported the fresh effort by prosecutors to “more fully bring him to justice” based on new evidence and testimony.

“The crimes committed by Epstein are horrific, and I am pleased that NY prosecutors are moving forward with a case based on new evidence,” he wrote.