Pope Francis has begged forgiveness for clerical child sex abuse and reiterated his wish to see justice served
He said no-one could fail to be moved by stories of those who "suffered abuse, were robbed of their innocence and left scarred by painful memories".
It is the first papal visit to Ireland in 39 years.
Later on Sunday, 500,000 people are expected to gather in Phoenix Park in Dublin as the Pope celebrates Mass to close the World Meeting of Families.
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His visit coincides with
The popemobile was not the dinky one that carried John Paul II and it buzzed quickly through the crowds.
But they got up close to Pope Francis - children on parents' shoulders; old people in wheelchairs, people in plastic ponchos and hats and mountain gear - captured by his warmth.
But those who had made the journey said it was worth it, in spite of the misery of the rain.
"We're here because we're Catholic and we're proud of it," said one woman.
The Marian shrine of Knock is a place of Catholic pilgrimage in the west of Ireland, where an apparition of Mary, the mother of Jesus Christ, is said to have appeared in August 1879.
About 1.5 million pilgrims from across the world visit the shrine every year.
Pope Francis arrived by plane at Knock at about 09:45 local time and greeted the crowds from his popemobile before going into the chapel to pray.
During the first day of his trip, Pope Francis used a speech at Dublin Castle to express his shame at the Catholic Church's failure to adequately address the "repellent crimes" of sex abuse by clergy.
He later he met eight survivors of sexual abuse, reportedly telling them he viewed clerical sex abuse as "filth".
Irish Prime Minister (Taoiseach) Leo Varadkar delivered a strong warning to the Pope to take action against clergy involved in child abuse and in keeping it secret.
Pope Francis told the crowds at Knock that the "open wound of abuses" committed by the Roman Catholic Church challenged it to be firm in the pursuit of truth and justice.
He said in his prayer to Mary, the mother of Jesus, he had "presented to her
A former top Vatican official has called on the Pope to resign, saying the pontiff knew about allegations of sex abuse by a prominent US cardinal for five years before accepting his resignation last month.
In an 11-page letter, Archbishop Carlo Maria Vigano said he had told Pope Francis in 2013 that Cardinal Theodore McCarrick had faced extensive accusations of sexually abusing lower-ranking seminarians and priests.
The Vatican has not responded to these claims - and Archbishop Vigano has not produced any written or other evidence to verify his conversation with Pope Francis.
Correspondents say the timing of his letter, released to coincide with the Pope's landmark visit to Ireland, has raised questions about whether this is a
On Saturday evening, Pope Francis presided over a Festival of Families concert in Dublin's Croke Park stadium, which drew a crowd of about 80,000 people.
The world-renowned tenor Andrea Bocelli, country singer Nathan Carter and acclaimed Irish singer Daniel O'Donnell were among those who performed.
The Ireland that the Pope is visiting is a different country to that which greeted Pope John Paul II in 1979.
Since the Polish pope's visit, there have been huge changes in public attitudes to social issues including abortion, contraception, divorce and same-sex marriage.
The country voted for constitutional change on
Pope Francis heard