The cardinal, who was too ill to return to Australia for questioning, is testifying to the royal commission via videolink from the Hotel Quirinale in Rome in front of a group of survivors from Ballarat.
Under questioning, he said child sex abuse had been an issue for centuries.
"The church has made enormous mistakes and is working to remedy those but the church in many places, certainly in Australia, has mucked things up, has let people down," he said.
"I'm not here to defend the indefensible."
He said the church in Australia had put in place procedures 20 years ago, namely the Melbourne Response and Towards Healing.
He said the problems in the church was not down to a "few bad apples" or the structure of the church.
"I think the faults overwhelmingly have been more personal faults, personal failures rather than structures,"
"Let me remind you that the reforms in '96/ '97 occurred within the old structures."
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Case for Mulkearns inquiry
Cardinal Pell said there was a case for a judicial tribunal to consider how Bishop Ronald Mulkearns handled clergy accused of child sexual abuse.
Cardinal Pell said he could not give "book, chapter and verse" about what Bishop Mulkearns knew and
did not act upon at particular times.
Bishop Mulkearns, who is now in his 80s and dying of cancer, was bishop in Ballarat, Victoria, from 1971 to 1997.
Cardinal Pell said there was a purpose to the way Bishop Mulkearns dealt with Gerald Ridsdale and other alleged pedophile priests.
A church-run judicial inquiry could consider how a bishop had handled sex abuse cases, he said.
He was asked by Gail Furness, SC advising the commission if he considered it appropriate for such a tribunal to consider the case of Bishop Mulkearns.
Dr Pell: "Yes there would certainly be a prime facie case. Yes."
Australian media 'manhandled'
Before giving evidence, Cardinal Pell arrived at the hotel via a side gate three hours early.
SBS Europe Correspondent Brett Mason said Cardinal Pell's security team had been heavy handed, "manhandling" him and a cameraman as they attempted to film the arrival.
However Cardinal Pell denied his security team was involved.
Cardinal Pell is sorry to hear of the incident with an SBS reporter and cameraman but it did not involve his security staff as has been reported, his office said in a statement.
"The Italian police are in charge of security outside and inside the hotel where the hearing is taking place and have been liaising with commission staff," the statement said.
Pell security allegedly manhandles SBS Europe Correspondent Brett Mason over filming:
'Expecting to get the same lies'
Cardinal Pell will be questioned over three to four days about what he knew of historic pedophile activity by priests when he served in Ballarat and Melbourne.
The Ballarat-born churchman is now in charge of the Vatican's finances.
The consensus among the visiting survivors is that the cardinal will still put the church before victims.
On the eve of his testimony it emerged he had tied a yellow ribbon at the Lourdes Grotto in the Vatican Gardens in support of Loud Fence, a movement that has spread worldwide after starting in Ballarat to show support for abuse victims.
"This is my gesture of support, especially for the people of Ballarat," Cardinal Pell said in a statement.
"I hope the coming days will eventually lead to healing for everyone."
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Andrew Collins, who was abused from the age of seven in Ballarat, said he would like to see the cardinal lay out what the church knew and admit it did things wrong in the past and now aimed to fix things.
"Unfortunately I think he will continue to say, 'I don't recall, I don't remember' and to put the welfare of the church before the welfare of the people the church has hurt," he told AAP.
The 47-year-old said the survivor group was not on a witch hunt but on a "quest for truth" to ensure such abuse never happened again.
Mr Collins said Cardinal Pell was a powerful figure in the church and had the capability to enact change to put victims first.
"If he did the right thing we'd applaud the man, we'd hug him, we'd say 'thank you'."
Cardinal Pell served in Ballarat between 1973 and 1984, presiding over a primary school where four Christian Brothers were pedophiles and living in a presbytery with Australia's worst pedophile priest, Gerald Ridsdale, in 1973.
Paul Levey, who was abused from the age of 12 by Ridsdale, said he found it hard to believe Cardinal Pell did not know what Ridsdale was up to when the pair had been so close.
The 47-year-old, wearing a bright red T-shirt bearing the slogan No More Silence, told AAP he had seen priests and bishops "trip up on their evidence" at other royal commission hearings.
But he believed Cardinal Pell would "make people dig for his answers".
Abuse survivor Peter Blenkiron, 53, said when he heard the cardinal's previous evidence before the commission he clenched his teeth so hard he cracked one of them.
"I'll try not to clench my teeth this time and try to breathe my way through it."
Survivor Phil Nagle said he was "expecting to get the same lies and deceit as we've always got" and for Cardinal Pell to "protect the brand".
