Speaking about his reason for being in Dublin, the World Meeting of Families, he called it "a prophetic witness" to the rich heritage of ethical and spiritual values, which it is a duty to cherish and protect and that the Church wants to support people as they try to respond, "faithfully and joyfully to their God given vocation in society".
The main objective of the trip to Ireland is to close a week-long worldwide Catholic gathering on the theme of the family that takes place every three years in a different city.
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.
Francis said he was committed to ridding the church of this "scourge" no matter the moral cost or amount of suffering.
Varadkar said it was time for a "new relationship between church and state in Ireland" and that abuse by priests and in church-run institutions were "stains on our state, our society and also the church".
He added: "In place of Christian charity, forgiveness and compassion, far too often there was judgment, severity and cruelty, in particular towards women and children and those on the margins".
He referenced the words of his predecessor, Benedict XVI, who in a letter to the Catholics of Ireland recognized the gravity of the situation of child sex abuse and demanded "truly evangelical, just and effective" measures in response to the betrayal of trust.
A devastating report earlier this month accused more than 300 priests in the U.S. state of Pennsylvania of abusing more than 1,000 children since the 1950s.
Francis will say the Angelus, spend some moments in private reflection and tour the crowds.
One of the victims of Fr Tony Walsh, a priest and serial abuser who assaulted hundreds of children over almost two decades, was also present but preferred to remain anonymous.
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Later in the day he is due to meet newlyweds and couples about to marry at St Mary's Pro cathedral in Dublin.
As Pope Francis prepares to celebrate Mass with half a million faithful in Dublin on Sunday afternoon, thousands are expected to take to the streets in protest over clerical sexual abuse amid an intensifying outcry over Church-related scandals spanning the globe.
Having been presented with flowers and vestments by children after his aeroplane Shepherd One touched down at Dublin Airport, Pope Francis was welcomed to the country by President Michael D Higgins at Áras an Uachtaráin (the president's residence).
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.
Mr Varadkar, Ireland's first openly gay prime minister, also used his speech to highlight an "increasingly diverse" Ireland, telling the Pope it was a "different country than it was 39 years ago".
The last papal visit to Ireland was by Pope John Paul II in September 1979.
Contraception, homosexuality, divorce and, most recently, abortion are now legal while Mass attendance has dropped dramatically.
Francis urged the Irish to do just that, to recognize that for all its failings, the Catholic Church has educated and cared for generations of Irish children in times of starvation and great poverty, when no one else would.
Meanwhile gardaí are urging all attending the Papal Mass in the Phoenix Park on Sunday to enter and leave using the colour coded routes as outlined as on their tickets.