The man chosen by the Federal Government to head its new mental health commission has decided not to take up the position after being accused of failing to properly investigate rape claims against a priest.

Monsignor David Cappo's appointment had been questioned by independent senator Nick Xenophon, who used parliamentary privilege to suggest he failed to investigate in a timely manner sex abuse allegations in the Catholic Church in South Australia.

Monsignor Cappo says he emphatically rejects any suggestion that he did not handle the abuse allegations with proper or due diligence.

But he says the matter has the potential to distract from his appointment to the Mental Health Commission and that he cannot allow that to occur.

Monsignor Cappo has also resigned as deputy chair of the Australian Social Inclusion Board.

He has declined an interview.

Monsignor Cappo led a review of South Australia's mental health system and provided recommendations on a range of other social issues in the state.

He was due to start his new role in January.

Mental Health Minister Mark Butler says the Government respects Monsignor Cappo's decision.

Mr Butler says he still believes Monsignor Cappo was the obvious choice to lead the Mental Health Commission given his experience and expertise.