Independent Senator Nick Xenophon has called on the Federal Government to reconsider the appointment of Monsignor David Cappo as chairman of its new Mental Health Commission.

Senator Xenophon claimed in Parliament last night that Monsignor Cappo has failed to investigate allegations of sexual abuse in the South Australian Catholic Church in a timely manner.

And he says if one of the priests who was allegedly involved in the sexual abuse is not relieved of his duties by noon today, he will name him in the Senate.

The sexual abuse claims were made by Archbishop John Hepworth, the primate of the Traditional Anglican Communion.

"Archbishop Hepworth was the victim of violent rapes perpetrated by three priests when he was a young boy studying to become a priest, and during his early years of priesthood," Senator Xenophon said.

And he claims the response of the Catholic Church in South Australia has been inadequate.

"I believe the weakness of that response can be traced back in part to Monsignor Cappo, who for reasons not fully explained, has failed to act in a timely and decisive manner on this important issue," he said.

Sorry, this audio has expired Listen to AM's report on the allegations

Senator Xenophon told Parliament Archbishop Hepworth reported his alleged sexual abuse to Monsignor Cappo and Adelaide Archbishop Philip Wilson in 2007.

"Mr Hepworth told these men he was repeatedly raped at various times over a 12-year period, beginning when he was 15," he said.

"But despite being told of the abuse in 2007, and receiving a detailed six-page statement in March 2008, David Cappo told John Hepworth this year that the investigation was still at, quote, 'a preliminary stage' because, incredibly, he claimed John had not lodged a formal complaint.

"I find this response to be as troubling as it is inadequate."

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Listen Duration: 9 minutes 11 seconds 9 m Archbishop John Hepworth talks to 891 ABC ( ABC Radio ) Download 4.2 MB

Monsignor Cappo recently retired as Social Inclusion Commissioner for the South Australian Government and will now head the national Mental Health Commission.

But Senator Xenophon questions this new appointment.

"I question whether it is appropriate for a senior religious figure like David Cappo, who has responded this way to allegations of serious sexual and psychological abuse, to be given the important role of chairman of the Federal Government's Mental Health Task Force," he said.

Senator Xenophon told the Chamber that two of the priests who allegedly abused Archbishop Hepworth are dead. But one is still alive.

"I am also calling for the Catholic Church in South Australia to immediately stand down this third priest from all his duties until these allegations are fully investigated," he said.

"I will give the Catholic Church in South Australia until midday [today] to remove this priest from his post, and to ensure he is not allowed contact with young people and children in his parish.

"If by midday this hasn't happened, I intend to name the priest in question here in the Senate.

"David Cappo and the Catholic Church should have acted years ago. If they don't act now, I will."

The Catholic Church has implored Senator Xenophon not to proceed with his naming threat.

It says there are many complex and sensitive issues involved, which the Senator needs to be made aware of as a matter or urgency.

It says it is happy to send legal advisers to meet with the Senator.