Staff and students have been on strike over the appointment of Professor Ana-Maria Cintra.
In articles in the two leading São Paulo newspapers, the cardinal reiterated that his decision, though breaking with tradition, did not breach the university's rules.
His priority, he said, is the "Catholic identity" of the PUC, which he said it is his desire to "evidence and strengthen".
At the same time the cardinal insisted that the role of a Catholic university is not to impose "a Catholic culture", but to be "a space of cultural dialogue".