0545 GMT September 23, 2019
The Irish prime minister earlier delivered a strong warning to the Pope to take action against clergy involved in child abuse and keeping it secret, BBC reported.
The papal visit, the first to the Irish Republic for 39 years, coincides with the World Meeting of Families.
It is a global Catholic gathering held every three years.
"I cannot 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," the Pope told political leaders and dignitaries at Dublin Castle.
"The failure of ecclesiastical authorities – bishops, religious superiors, priests and others – adequately to address these repellent crimes has rightly given rise to outrage, and remains a source of pain and shame for the Catholic community," he said.
"I myself share those sentiments."
Earlier this week, in a letter to the world's 1.2bn Roman Catholics, the Pope condemned the "atrocities" of child abuse and clerical cover-ups.
He was speaking after Varadkar said the failures of the church, the state and wider society had created a "bitter and broken heritage for so many, leaving a legacy of pain and suffering".
"Magdalene Laundries, mother and baby homes, industrial schools, illegal adoptions and clerical child abuse are stains on our state, our society and also the Catholic Church," he said.
"People kept in dark corners, behind closed doors, cries for help that went unheard.
"Above all, Holy Father, I ask to you to listen to the victims and survivors."
Varadkar said there could be zero tolerance for those who abuse children or who facilitate that abuse and that from words action must flow.