Independent Senator Nick Xenophon says he has named a priest at the centre of an alleged seminary rape scandal because the Catholic church failed to stand the man down while investigating the allegations.

Speaking under parliamentary privilege last night, Senator Xenophon named the priest as Monsignor Ian Dempsey, a parish priest in the Adelaide suburb of Brighton.

Senator Xenophon said there were allegations that Monsignor Dempsey raped the Archbishop of the Traditional Anglican Communion, John Hepworth, more than 40 years ago.

"The people of the Brighton parish have a right to know that for four years allegations have been outstanding that priest Ian Dempsey raped John Hepworth, and that church leadership has failed to make appropriate inquiries into this matter, and that church leadership has failed to stand this priest down as a matter of course while inquiries take place," Senator Xenophon said.

"I now call on the Catholic Church in South Australia to act with the fairness and sense of urgency that's been sadly lacking for the last four years.

"This issue needs to be resolved in the interests of John Hepworth and all victims of sexual abuse. Sexual abuse flourishes because people keep secrets."

The Archdiocese of Adelaide says it is grossly unfair for Senator Xenophon to identify the priest when he has denied the allegation and before it has finished investigating the matter.

The church sent Senator Xenophon a lawyer's letter on Tuesday imploring him not to name the priest, but the senator said he had no choice.

Accused under parliamentary privilege: Monsignor Ian Dempsey ( www.brightonparish.com.au )

Sorry, this audio has expired Senator names priest involved in abuse allegations

The alleged victim, Archbishop John Hepworth, has said he was repeatedly raped by three priests over a 12-year period while training in a Catholic seminary.

Archbishop Hepworth said he did not want Senator Xenophon to name the priest in Parliament.

"I have suggested to him that instead of naming the priest tonight, which brings things to some sort of climax but maybe not one that solves any problems, that he write to Archbishop Wilson suggesting to him that it's probably important enough to request the priest stand aside while that inquiry of the QC proceeds," he said.

"If indeed the Archbishop agrees to ask the priest to stand aside, then there is no need to name him.

"My allegations were a greater story than just this one priest. This treatment of this priest is only one part of that story.

"As long as the process goes on that is fair and just, I will be comfortable with that."

On Tuesday the Catholic Church responded to Senator Xenophon's threat to name the priest with a legal letter in which it said: "The priest concerned has categorically denied the allegations."

"Objectively speaking, it is not irrelevant that he has been a priest of good standing in the archdiocese for almost 50 years," the letter said.

"In those circumstances, any decision to suspend the priest concerned would be unjustifiable as a matter of canon and civil law."

But Archbishop Hepworth disagreed, saying the priest should be forced to step down.

"In the Catholic Church generally in Australia, bishops do stand priests aside or request they stand aside while allegations are investigated," he said.

"I can't see how there can be any sort of law that would in fact prevent that request being made."

Archbishop John Hepworth had asked Senator Nick Xenophon not to name the priest.

Sorry, this audio has expired Church defends treatment of abuse allegations

Senator Xenophon also called on the Federal Government to reconsider its appointment of Monsignor David Cappo as chairman of its new Mental Health Commission, claiming he failed to properly investigate the sexual abuse allegations.

A spokeswoman for Mental Health Minister Mark Butler said the Government stands by its decision to appoint Monsignor Cappo as he was the obvious choice.

But Senator Xenophon said the Adelaide diocese has not conducted a proper investigation and should be held responsible.

"I will make it very clear that everyone has a presumption of innocence, but the issue here is that Archbishop Hepworth approached the Catholic Church in South Australia... over four years ago about this," he said.

"He made a written complaint over three years ago, after what I think was an unsatisfactory process to begin with.

"What was offered to Archbishop Hepworth was really not satisfactory. So the Catholic Church in South Australia has itself to blame if this course continues.

"This man can be stood down on administrative leave pending an investigation."

Archbishop Hepworth said earlier on Tuesday he was still hopeful of a resolution.

"Only the church can heal what the church has broken, and if victims cannot approach the church they do not heal," he said.