The decree quoted the pontiff as saying that such cases would fall under an existing proviso in canon law allowing for prelates to be sacked for "serious reasons."
"I intend to specify that among these so-called 'serious reasons' is the negligence of bishops in the exercise of their functions, especially in cases of sexual abuse of minors or vulnerable adults," Francis wrote.
Vatican spokesman Federico Lombardi said the pope also set up a body of lawyers to assist him in decisions that could require the dismissal of a bishop.
In the decree -- an apostolic letter with a status in Latin called "motu proprio" ("on his own impulse") -- the Pope emphasised that the Church "loves all its sons, but cares for and protects with special attention those who are weakest and defenceless."
This is why priests, and especially bishops, should demonstrate "particular diligence in protecting the weakest among those who are entrusted to them," the pope said.
A string of historic paedophilia cases in North America and Europe has unleashed widespread criticism of the Catholic hierarchy, including allegations that in some cases bishops were aware of sexual predators among
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the priesthood but failed to curb them.
Pope Francis took office promising a crackdown on cover-ups and a zero-tolerance approach to abuse itself, which he famously described as being akin to taking part in a Satanic mass.