A Vatican-sponsored World Meeting of Families that opened on Tuesday ends Sunday in Dublin.
The pope wrote a letter to the world's 1.3 billion Catholics vowing to prevent future "atrocities" but conceding no efforts "to fix the harm done will ever be sufficient".
"I can not fail to acknowledge the grave scandal caused in Ireland by the abuse of young people by members of the Church charged with responsibility for their protection and education", Francis said during his remarks in Dublin Castle.
Pope Francis said Saturday that the "failure of ecclesiastical authorities" to address sexual abuse has "rightly given rise to outrage", his first acknowledgment during his trip to Ireland of the traumas here that have radically diminished the Roman Catholic clergy's once-towering authority.
"I'm delighted he is coming, I think it makes a great change from the last few years of bad news for the Church", said Dubliner Kyle O'Sullivan.
Pope Francis will meet victims of clergy sexual abuse during his visit to Ireland this weekend, the Vatican says.
"Far too often there was judgement, severity and cruelty. people kept in dark corners, behind closed doors, cries for help that went unheard", he added.
"Holy Father, I ask that you use your office and influence to ensure this is done here in Ireland and across the world", Varadkar said.
A devastating report earlier this month accused more than 300 priests in the USA state of Pennsylvania of abusing more than 1,000 children since the 1950s.
Amnesty Ireland Executive Director Colm O'Gorman said on Twitter that Francis "had the ideal opportunity to address the abuse issue".
Clerical sex abuse victims call for a redress scheme from the Catholic Church.
They set children's shoes on the pavement, each representing a child who had been abused by priests.
Francis followed his promise with a 90-minute meeting with eight survivors of both clerical and institutional abuse and prayed quietly before a candle lit for victims in Dublin's cathedral.
The Argentinian Pope remains highly popular in Ireland, and tens of thousands of people are expected at Dublin's Croke Park stadium Saturday evening for a concert-style event.
He was then driven in a Skoda rapid auto to "Áras an Uachtaráin", the residence of the Irish president, Michael Higgins where the pair met and the Pope signed a book of remembrance.
The Popemobile then travelled along Westmoreland Street and Dame Street before dropping the Pope off at Capuchin Day Centre where he met with those affected by the homelessness crisis in Dublin.
But the defining moment of the first papal visit to Ireland in almost 40 years did not take place on camera.
When Pope John Paul II visited Ireland in 1979, divorce and contraception were illegal in the country.
Redmond said the pope "lifted his hands to his head in shock" during the closed-door meeting after hearing stories of ill-treatment in Church-run Mother and Baby Homes.
He said he is "very conscious" of the circumstances of the most vulnerable and emphasized the goodness of the child, which he said is "a precious gift of God, to be cherished, encouraged to develop his or her gifts, and guided to spiritual maturity and human flourishing".
During a speech at Dublin Castle yesterday the Irish Taoiseach also urged the Pontiff, 81, to listen to victims of historic sex abuse.