Francis said he was committed to ridding the church of this "scourge" no matter the moral cost or amount of suffering.
"There can only be zero tolerance for those who abuse innocent children or who facilitate that abuse", said Varadkar.
Francis, facing sexual abuse crises in several countries, wrote an unprecedented letter to all Catholics this week asking each one of them to help root out "this culture of death" and vowing there would be no more cover ups.
"With regard to the most vulnerable, 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", he said.
Francis' trip to Ireland, the first by a pope in 39 years, has been overshadowed by renewed outrage over the Catholic Church's systemic failures to protect children, following revelations of sexual misconduct and cover-up in the USA church hierarchy, a growing crisis in Chile and the prosecutions of top clerics in Australia and France. "I myself share those sentiments".
He referred to an investigation in the U.S. state of Pennsylvania that found that more than 1,000 identifiable minors had been abused by 300 priests.
"Ireland has become a very different place in the last 40 years and our relationship with the Church has changed principally because of so many revelations that have occurred around child sex abuse".
"It's a good crowd, but wouldn't be near what you'd get for (Saint) Patrick's Day", said Christy Moore, 59, referring to Ireland's national holiday as he sold papal flags wearing an "I love Pope Francis" hat.
An Alitalia flight carrying the pope, his entourage and the Vatican media corps touched down at Dublin airport just before 10.30am on Saturday for only the second papal visit to Ireland.
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"We feel hopeful there will be more movement from the Church", Redmond said in a statement put out by the Coalition of Mother and Baby Home Survivors.
But in his speech at Dublin Castle, he said both church and state had a history of "sorrow and shame", and he urged the pope to ensure that victims of sex abuse find "justice and truth and healing".
The pontiff will travel up O'Connell Street, Westmoreland Street and Dame Street at around 4.15pm this afternoon.
Varadkar said the Magdalene Laundries, where unmarried mothers were incarcerated, and other institutions where abuse was carried out, were "stains on the Irish state and society and also on the church".
The Supreme Pontiff met privately for 90 minutes with eight survivors of abuse at the hands of the Catholic Church.
He will begin the two-day visit by meeting Ireland's President Michael D. Higgins and Varadkar, who has promised to challenge the pope to do more in dealing with the abuse crisis.
Spokesman Greg Burke told reporters at a briefing on the August 25-26 trip the details of the meeting would not be announced until after it was over and it would be up to the victims if they wanted to speak afterwards. They have overturned a constitutional ban on abortion and legalized divorce, contraception and same-sex marriage.
On Sunday he is due to visit the Marian shrine at Knock, where a vision of the Virgin Mary is said to have appeared to villagers in 1879, before conducting a Papal Mass in Phoenix Park.
In the evening he will join 82,000 pilgrims at a musical festival in the landmark Croke Park Gaelic Athletic Association stadium.
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In the second blow to the Rivera's defense, Crookham-Johnson denied Richard's request for a more "attainable" bond for his client. Rivera alleged he blacked out at some point and woke up at an intersection in rural Poweshiek County, court documents state.
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