The pope has so far refused to respond to allegations made last month that he for years covered up sexual abuse allegations against a prominent US cardinal.
"With people who lack goodwill, with people who seek only scandal, who seek only division, who seek only destruction, even within the family: [there is nothing but] silence. And prayer," Francis said during a service at St Martha's, the boarding house where he stays.
Among some ultra-conservative Catholics, the pope is regarded as a dangerous progressive who is more interested in social issues than traditional Church matters.
Pope's rightwing rivals on the attack over abuse claims
His comments came after Archbishop Carlo Maria Vigano, a former Vatican envoy to Washington, claimed in August that Francis ignored sexual abuse allegations against US cardinal Theodore McCarrick for five years.
The timing of the letter's release right in the middle of Francis's landmark trip to Ireland immediately raised speculation about a campaign against the Argentine pontiff.
But so far, Francis has remained silent, refusing to address the allegations and saying only that Vigano's missive "speaks for itself".
On Saturday, Vigano launched a fresh attack, accusing the pope of knowing full well that he was meeting an arch-conservative opposed to gay marriage during a 2015 visit to the United States.
The Vatican said at the time that the pope met Kim Davis, a Kentucky clerk who has refused to sign gay marriage certificates, during a reception along with 'dozens of other guests' at the embassy in Washington.
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