He alleged that Cardinal Pell, who was appointed by Pope Francis in February 2014 to make the Vatican's finances more transparent, went on to ask what it would cost to buy his silence.
The cardinal was also accused of helping to move the disgraced priest between parishes.
Australian Cardinal George Pell
Cardinal Pell said he had been following the proceedings and was "horrified once again by survivors' accounts of the abuse they have suffered", but denied trying to bribe David Ridsdale or his family or "offer any financial inducements for him to be silent".
"Over the last 24 hours I have been accused of being complicit in the moving of a known paedophile, of ignoring a victim's complaint and of bribery," he said in a statement.
"These matters again require an immediate response and it is important to correct the record, particularly given the false and misleading headlines."
Cardinal Pell, who is not accused of any sexual abuse, said at the time of the discussion the police were already aware of allegations against Gerald Ridsdale and were investigating.
"Then, and now, I supported these police investigations. I have previously made a sworn denial of these allegations and I reiterate that denial," he added.
"I never moved Ridsdale out of Mortlake Parish. I never moved him anywhere. I would never have condoned or participated in a decision to transfer Ridsdale in the knowledge that he had abused children."
The commission has heard harrowing allegations of child abuse involving places of worship, orphanages, community groups and schools.
The hearings this week have focused on shocking abuse in the 1970s in the regional town of Ballarat.
It heard that every male child aged between 10 and 16 at the St Alipius primary school, where Ridsdale and other paedophile priests worked, was thought to have been molested.
One survivor held up a photograph of his class of 33 boys and said 12 of them had committed suicide.
Another victim, Gordon Hill, described what he called the "horror rooms" at the St Joseph's Home orphanage where he was sexually abused from the age of five. He said one of the nuns would tell him: "Father wants to cleanse you."
Nicky Davis, leader of the Survivors Network of those Abused by Priests, said Cardinal Pell should appear before the commission again.
"It is vastly inappropriate to respond to sworn evidence by courageous survivors with a media statement that callously dismisses their experience," she told reporters.
"If Cardinal Pell is at all genuine in his claims to recognise the seriousness of the crime of sexual violation of defenceless children, he would voluntarily return to Australia to give evidence under oath to the royal commission."
Cardinal Pell said he was committed to complete cooperation with the commission and would "address in full all matters it wishes to raise in any statement requested from me before I make any further comment".