"In which may yet revive the consecrated Seed of those Romans"

(Canto 15, lines 76-77)

Dante does not directly say that his family stems from the Romans rather than the Fiesolans, but maybe we are supposed to understand that from his talk of "the beasts of Fiesole" and "the consecrated seed of those Romans". Dante's private mythology is full of the idea of the chosenness of Rome - see for example the Convivio, book 4, chapter 5 for his thoughts on the divine nature of Rome and its ruling lineage.