In a statement yesterday Dempsey denied the accusations.
"I am aware of John Hepworth's unsubstantiated allegations against me through an inquiry instigated by the Archbishop of Adelaide," he said.
"I have made it clear in writing to the inquiry that I categorically deny the allegations, which, I note, are said to relate to events that occurred some 45 years ago, and they have nothing at all to do with underage people."
Xenophon has been accused of denying the monsignor natural justice.
Yesterday the South Australian police said they would inquire into the allegations.
Dempsey, now the parish priest at Brighton, was Vicar-General of the Archdiocese of Adelaide for five years and had been director-general of the Navy's chaplains. He is also an Officer of the Order of Australia.
He is one of three priests accused of raping Archbishop John Hepworth over a 12-year period beginning when he was a 15-year-old trainee priest. The other two priests are dead, and the Melbourne Catholic Church issued an apology and made financial compensation to Hepworth, who had left the Church after the abuse to become an Anglican. He is now Archbishop of the Traditional Anglican Communion, an international movement that split from the authority of the Archbishop of Canterbury on issues ranging from homosexuality and the ordination of women, and which is now courting ties with the Papacy.
Xenophon on Monday warned the Adelaide Archdiocese to stand Dempsey down pending an investigation of the allegations, or have the priest publicly named under privilege in the Senate.
Xenophon said Hepworth had spoken to Cappo about the alleged abuse in 2007, had provided a detailed six-page statement in March 2008 and had offered to provide a copy of the Melbourne Church's inquiry.
But Cappo had told the archbishop this year that the investigation was still at a preliminary stage because he had not lodged a formal complaint.
Xenophon told the Senate on Tuesday night that the Church had not followed the protocols of other churches under which a priest facing similar allegations would be stood down while an investigation was made.
"The allegations are serious," Xenophon said. "They are made by a man with credibility and they have not been appropriately acted upon by the Catholic Church in South Australia."
The archdiocese said Dempsey had categorically denied the allegations.
"It is not irrelevant that he has been a priest of good standing in the archdiocese for almost 50 years," it said in a legal letter to Xenophon. "In those circumstances, any decision to suspend the priest concerned would be unjustifiable as a matter of canon and civil law."
The archdiocese said it was "grossly unfair" to identify Dempsey before it had finished investigating.
Xenophon was cautioned on the use of parliamentary privilege by Senate president John Hogg and later criticised by Coalition senators for undermining the presumption of innocence.
