The pontiff made the comments at the Marian shrine in Knock during the second day of an historic trip to the Republic of Ireland.
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.
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Hundreds of thousands of people have gathered in Phoenix Park in Dublin as the Pope celebrates Mass, closing the World Meeting of Families.
His visit coincides with the the global Catholic gathering, which is held every three years.
Pope’s people on Phoenix pilgrimage – By Leanna Byrne in Dublin
Grey clouds, light rain and soft gospel music hangs in the air above the revellers making their mini-pilgrimage from the city centre to Phoenix Park.
Scrums of people wearing rain jackets, hats and backpacks are directed by bunting, bobbing and weaving up to their allocated space, set out alphabetically.
Deck chairs have already been wedged into place and sandwiches or other more exotic dishes – I did see a salmon curry – have already been taken out of bags.
The crowd are happy to be here – all have booked their tickets to hear what Pope Francis has to say.
Like the pilgrims at Croke Park on Saturday night, these are Pope Francis’s people.
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.
Knock was also visited by Pope John Paul II during his visit to Ireland in 1979.
‘Repellent crimes’
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 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 in particular all the victims of abuse of whatever kind committed by members of the Church in Ireland”.
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 co-ordinated attack from traditionalists within the Catholic hierarchy who oppose Pope Francis.
‘Modernised Ireland’
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 same sex-marriage in 2015 and voted overwhelmingly to overturn its strict abortion law in May.
Pope Francis heard Mr Varadkar, a gay man, speak out against the traditional Catholic teaching on the family.
The taoiseach said that the Republic of Ireland had modernised its laws, “understanding that marriages do not always work, that women should make their own decisions and that families come in many forms” – including those headed by a lone parent, same-sex parents or parents who are divorced and remarried.
You can follow minute-by-minute updates on the Pope’s visit here on the BBC News website.
Switch on for Sunday’s BBC Newsline showing highlights from the visit at 22:30 BST.
On BBC Radio Ulster, join Seamus McKee for a special extended The Sunday News at 13:00.