Pope Francis has said that the Catholic Church will never again treat abuse allegations without "seriousness and promptness", calling on abusers to hand themselves in to police.

"The Church will never seek to hush up or not take seriously any case," the pope said in his annual address to the Church's governing Curia at the Vatican.

"Let it be clear that before these abominations the Church will spare no effort to do all that is necessary to bring to justice whosoever has committed such crimes".

The Pope as recently as Wednesday accepted the resignation of a US auxiliary bishop over his "misconduct" with a minor.

"It is undeniable that some in the past, out of irresponsibility, disbelief, lack of training, inexperience, or spiritual and human short-sightedness, treated many cases without the seriousness and promptness that was due.

"That must never happen again. This is the choice and the decision of the whole Church."

Pope Francis also called on for anyone who has committed child abuse, including priests, to hand themselves over to justice.

"To those who abuse minors I would say this: convert and hand yourself over to human justice, and prepare for divine justice," he told Curia.

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Pope Francis last week removed two prominent cardinals from his inner circle months after they were tainted by paedophile scandals and ahead of a Church-wide meeting on the "protection of minors" next year.

Australian Cardinal George Pell and Chilean Cardinal Francisco Javier Errazuriz were both removed from the so-called C9 Council of Cardinals, an international advice body set up by Pope Francis himself, the Vatican said on 12 December.

The last time the C9 met in September, Cardinal Errazuriz, who is accused of ignoring reports of abuse in Chile, and Cardinal Pell, who faces charges in Australia related to historical child sexual offences, were both absent, and the council said it was considering restructuring.

Despite being removed from the C9, Cardinal Pell, 77, remains in charge of Vatican finances, the third most powerful position in the church.

The Church has been hit by a series of child abuse scandals in recent years, with widespread allegations of cover-ups, including against the pope himself.

Pope Francis told the Curia that there were still "consecrated men... who abuse the vulnerable, taking advantage of their position and their power of persuasion."

"They perform abominable acts yet continue to exercise their ministry as if nothing had happened. They have no fear of God or his judgement, but only of being found out and unmasked."

"Often behind their boundless amiability, impeccable activity and angelic faces, they shamelessly conceal a vicious wolf ready to devour innocent souls."