Pope Francis' finance minister has denied an allegation that he offered a bribe to a victim of clergy abuse to protect a pedophile priest.

The allegation against Cardinal George Pell was made under oath on Wednesday at a government inquiry known as the Royal Commission into Institutional Responses to Child Sex Abuse in Australia.

The allegation has dogged the Australian cardinal for years. Commission chairman Peter McClellan said he expected his inquiry will make findings about cover-up allegations surrounding Pell. Pell has denied any wrong doing.

David Ridsdale, the nephew of convicted pedophile priest Gerald Ridsdale, testified at the inquiry in the Victoria state town of Ballarat that he told Pell in a telephone conversation in 1993 about the abuse he had suffered as a child at the hands of his uncle.

David Ridsdale told the inquiry that Pell, then a priest and a family friend, said: "I want to know what it will take to keep you quiet."

Ridsdale told the inquiry that Pell started talking about Ridsdale's growing family and said that Ridsdale may soon have to buy a car or house.

Risdale said he hung up the phone and immediately told his two sisters that Pell "just tried to bribe me."

Pell said in a statement from the Vatican that the uncle was already under police investigation over pedophilia allegations when David Ridsdale called, and that Pell had cooperated with that investigation.

"I was and remain extremely sympathetic to David Ridsdale who because of his uncle suffered horrible abuse. I continue to regret the misunderstanding between us," Pell said in the statement.

"At no time did I attempt to bribe David Ridsdale or his family or offer any financial inducements for him to be silent," Pell said.

McClellan said that the commission would request a statement from Pell regarding child abuse cover-up allegations in Ballarat. Pell said he was "committed to complete cooperation with the Royal Commission."

"I will address in full all matters it wishes to raise in any statement requested from me before I make any further comment," Pell said.