Labor Secretary Alex Acosta doesn’t plan to resign over his association with financier Jeffrey Epstein and will hold a news conference on July 10, a Department of Labor official said.

Acosta has come under increased pressure since Epstein’s indictment for sex trafficking and conspiracy was revealed on July 8. In 2008, Epstein pleaded guilty to state charges in Florida in order to resolve similar allegations under a lenient deal with Acosta, then a U.S. attorney. The agreement allowed Epstein to...