ESSEN, Germany—German Chancellor Angela Merkel called for the prohibition in some situations of the full facial veil, toughening her rhetoric toward Muslim immigrants as she sought to shore up her party’s conservative flank at its annual convention on Tuesday.

“We show our face in interpersonal communication,” Ms. Merkel told delegates of her Christian Democratic Union party to some of the strongest applause of her more than hourlong speech. “Because of this, the full veil is unacceptable for us. It should be banned wherever...