Washington (CNN) House Oversight Chairman Elijah Cummings wants Labor Secretary Alexander Acosta to testify at a hearing later in the month on his handling more than a decade ago of a plea deal for multi-millionaire Jeffrey Epstein who now faces new charges in New York for human trafficking.

The request comes as top congressional Democrats have called for Acosta to resign over the matter after federal prosecutors unsealed a criminal indictment on Monday charging Epstein with having allegedly operated a sex trafficking ring in which he sexually abused dozens of underage girls.

In a letter to Acosta on Wednesday, Cummings and Democratic Rep. Jamie Raskin, who chairs the panel's subcommittee on civil rights and liberties, invite the labor secretary to testify in a hearing on July 23.

The letter states that "the hearing will examine your actions as US Attorney for the Southern District of Florida in authorizing a non-prosecution agreement for Jeffrey Epstein, as well as the finding by a federal court that you violated the Crime Victims' Rights Act by keeping this non-prosecution agreement secret from the victims of Mr. Epstein's crimes."

Senate Democratic leader Chuck Schumer and House Speaker Nancy Pelosi, along with a host of other congressional Democrats, have called for Acosta's resignation this week. Congressional Republicans have not joined in the calls, however, and the labor secretary has pushed back.

Read More