The Pope said that abuse of children was like "leprosy" infecting the Church, according to the Italian La Repubblica newspaper.
He vowed to "confront it with the severity it demands".
But a Vatican spokesman said the quotes in the newspaper did not correspond to Pope Francis's exact words.
The BBC's David Willey in Rome says there is often a studied ambiguity in Pope Francis' off-the-cuff statements.
He wants to show a more compassionate attitude towards Church teaching than his predecessors, but this can sometimes cause consternation among his media advisers, our correspondent adds.
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