Pope Francis has said he would not respond to explosive accusations by a former top Vatican official that the pontiff had covered up sexual abuse, saying dismissively that the document containing the allegations "speaks for itself".

Key points: Pope meets privately with abuse victims, makes public apology for "state of shame"

Pope meets privately with abuse victims, makes public apology for "state of shame" This is the first papal visit to Ireland in almost four decades

This is the first papal visit to Ireland in almost four decades Pope accused of knowing allegations of sex abuse by prominent US cardinal for five years

Talking to reporters aboard the plane returning to Rome from Dublin, Pope Francis said he would "not say one word" on the 11-page document, in which the former official says the pontiff should resign.

Pope Francis said journalists should read the document carefully and decide for themselves about its credibility.

The official accused the Pope of having known of allegations of sex abuse by a prominent US cardinal for years.

The document by Archbishop Carlo Maria Vigano, the former Vatican ambassador to Washington, was an unprecedented broadside against the Pope by a Church insider.

Pope Francis accepted Theodore McCarrick's offer to resign late last month. ( AP: Jonathan Newton )

"I read that statement this morning. I read it and I will say sincerely that I must say this, to you [the reporter] and all of you who are interested: read the document carefully and judge it for yourselves," he said.

"I will not say one word on this. I think the statement speaks for itself and you have sufficient journalistic capacity to reach your own conclusions."

Archbishop Vigano gave the bombshell statement to conservative Roman Catholic media outlets during the Pope's visit to Ireland, which was dominated by the Church's sexual abuse in that country and others around the world.

He accused a long list of current and past Vatican and US church officials of covering up the case of former cardinal Theodore McCarrick, the retired archbishop of Washington DC.

McCarrick, 88, resigned last month in disgrace and was stripped of his title after allegations that he had abused a minor nearly 50 years ago, and also forced adult male seminarians to share his bed.

Pope Francis has been met by protesters during his Ireland trip. ( AP: Matt Dunham )

In the letter, Archbishop Vigano accused the former Vatican secretaries of state under the previous two popes of ignoring detailed denunciations against McCarrick for years.

He said Pope Benedict XVI eventually sanctioned McCarrick in 2009 or 2010 to a lifetime of penance and prayer.

Pope apologises for 'state of shame' in Ireland

Pope Francis delivers mass at Phoenix Park in Dublin. ( AP: Matt Dunham )

Speaking in Ireland during the first papal visit to Ireland in almost four decades, Pope Francis asked forgiveness for the multitude of abuses suffered by victims there at the hands of the church over decades, as he concluded a tour of the once deeply Catholic country.

After meeting privately with abuse victims on Saturday, the Pope apologised to mothers estranged from their children in church-run homes, children abused by priests and those exploited in religious schools, calling it a "state of shame".

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"To survivors of abuse of power, conscience and sexual abuse, recognising what they have told me, I would like to put these crimes before the mercy of the Lord and ask forgiveness for them," he said at a church service attended by more than 100,000 people at Dublin's Phoenix Park.

"We apologise for some members of the hierarchy who did not take care of these painful situations and kept silent."

Years of sexual abuse scandals have shattered the credibility of the church, which dominated Irish society four decades ago.

In the past three years, Irish voters have approved abortion and gay marriage in referendums, defying the Vatican.

The declining influence of the Catholic Church has been demonstrated by crowds far smaller than those that met Pope John Paul II during the last papal visit in 1979, when more than three-quarters of Ireland's population turned out.

While 500,000 people snapped up tickets to see Pope Francis say mass, local media quoted police recording the numbers as estimating some 130,000 arrived in the rain at the same spot where Pope John Paul II stood 39 years ago.

Followers greet Pope Francis as he arrives at the Croke Park Stadium in Dublin. ( AP: Aaron Chown )

'Give this man a chance'

Pope Francis, facing sexual abuse crises in several countries, wrote an unprecedented letter to all Catholics last week asking each one of them to help root out "this culture of death" and vowing there would be no more cover-ups.

Some who turned out for him in the Irish village of Knock, where a group of locals in 1879 said they saw an apparition of the Virgin Mary, said Pope Francis should be given time to deal with the abuse issues that have rocked the church for decades.

"People have to give this man a chance, he's trying his best," Carmel Lane, who travelled from County Longford in the Midlands, said.

However thousands of people joined survivors, their families and supporters at an event elsewhere in Dublin as the Pope said mass to stand in solidarity with those who had suffered.

"It [the visit] has been very, very painful," said Graham Mills, 52, who was sexually abused as a child by a member of the Christian brothers religious order and travelled from Northern Ireland to join the protest.

"I think Pope Francis is probably a very decent human being. But yesterday I was very disturbed by the big celebration for him knowing the lives that have been destroyed."

Reuters/AP