Interviewed by Italy's La Repubblica daily, Francis also condemned child sex abuse as a "leprosy" in the Church and cited his aides as saying that "the level of paedophilia in the Church is at two percent".
"That two per cent includes priests and even bishops and cardinals," the pope was quoted as saying.
Asked whether priests might one day be allowed to marry, Francis pointed out that celibacy was instituted "900 years after Our Lord's death" and that clerics can marry in some Eastern Churches under Vatican tutelage.
But Vatican spokesman Federico Lombardi said the quotations in the newspaper on the existence of paedophile cardinals and the possible reform of priestly celibacy did not correspond to what the pope actually said.
"This is not at all an interview in the normal sense of the word," he said, accusing the newspaper of "manipulating ingenuous readers".
The interview was the third in a series with the 90-year-old founder of the La Repubblica daily, Eugenio Scalfari, a famous journalist and known atheist.
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