Cardinal George Pell was accused of telephoning a victim of paedophile priest Gerald Ridsdale and asking what it would take to keep him quiet in 1993.
The allegation was made at a government inquiry into Institutional Responses to Child Sex Abuse in Australia.
The victim, David Ridsdale, the priest's nephew, told the panel the clergyman said: "I want to know what it will take to keep you quiet."
In a statement released by the Vatican Cardinal Pell said he would co-operate in full with the inquiry but added the allegations were not true.
"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," he said.
"At no time did I attempt to bribe David Ridsdale or his family or offer any financial inducements for him to be silent."
The inquiry is now expected to ask the Cardinal, who runs the finance department at the Holy See, for an official statement.
He added that he was "committed to complete cooperation with the Royal Commission," and that he would "address in full all matters it wishes to raise in any statement requested from me before I make any further comment".