ROME—Pope Francis told a gathering of bishops from around the world that the Catholic Church is being persecuted through accusations—an apparent allusion to clerical sex-abuse scandals that have undermined the credibility of the papacy and church hierarchy over the course of this year.

Addressing the closing session of a synod of bishops at the Vatican on Saturday, the pope repeated warnings he has made in recent weeks against the “Great Accuser,” or the devil, who “in this moment is accusing us strongly, and this accusation...