Dublin, Ireland (CNN) Pope Francis says he "will not say a single word" on an archbishop's call for him to resign over his handling of sexual abuse allegations against a prominent US cardinal in 2013.

In a statement seen by CNN on Sunday, Archbishop Carlo Maria Vigano, a former Vatican ambassador to the United States, said he told the Pope about allegations of sexual abuse against then-Cardinal Theodore McCarrick five years ago, but the Pontiff did nothing about it.

McCarrick, 88, who once led the Archdiocese of Washington and was a force in American politics, resigned as cardinal last month after a decades-old allegation of sexual abuse of a teenage altar boy. The Pope also ordered McCarrick's suspension from public ministry.

Vigano called for the Pontiff to resign over his failure to act. "Pope Francis must be the first to set a good example to cardinals and bishops who covered up McCarrick's abuses and resign along with all of them," Vigano said in a lengthy statement dated August 22.

Speaking to the press Sunday on his flight back to Italy from Ireland, Pope Francis said, "I will not say a single word on this," although he added that after some time passes, "I may speak."

The Pope told reporters he believes the statement from Vigano speaks for itself. "I read the statement this morning, and I must tell you sincerely ... read the statement carefully and make your own judgment," he said.

'Serial predator'

"He [Pope Francis] knew from at least June 23, 2013, that McCarrick was a serial predator," Vigano said in his statement, adding, "although he knew that he was a corrupt man, he covered him to the bitter end."

"It was only when he was forced by the report of the abuse of a minor, again on the basis of media attention, that he took action [regarding McCarrick] to save his image in the media," Vigano continued.

A source close to Vigano -- who retired in 2016 at age 75 -- confirmed the letter is genuine.

Photos: In pictures: Pope Francis visits Ireland Pope Francis arrives at the closing Mass of his Ireland visit at Phoenix Park in Dublin, Ireland on Sunday, August 26, 2018. Hide Caption 1 of 23 Photos: In pictures: Pope Francis visits Ireland Clerical sex abuse protesters assemble at the General Post Office in Dublin before marching to the Garden of Remembrance during the Pope's visit to Ireland on Sunday. Hide Caption 2 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis celebrates Mass at Phoenix Park in Dublin, Ireland, on Sunday. Hide Caption 3 of 23 Photos: In pictures: Pope Francis visits Ireland An aerial view of the crowd at Phoenix Park in Dublin as Pope Francis celebrates the closing Mass at the World Meeting of Families on Sunday. Hide Caption 4 of 23 Photos: In pictures: Pope Francis visits Ireland An aide adjusts Pope Francis' cape as he speaks at the Knock Shrine in Knock, Ireland, on Sunday. Hide Caption 5 of 23 Photos: In pictures: Pope Francis visits Ireland People wait for the arrival of Pope Francis in front of the Knock Shrine on Sunday. Hide Caption 6 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis passes by a banner of a protester as he leaves St. Mary's Pro-Cathedral in Dublin on Saturday. The Pope spoke of his shame over the "appalling crimes" of historic child abuse in the Catholic Church and said outrage was justified. However, he failed to specifically mention the current scandal over a US grand jury report documenting at least 1,000 cases of clerical pedophilia. Hide Caption 7 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis prays at St. Mary's Pro-Cathedral in Dublin on Saturday. Hide Caption 8 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis waves to the waiting crowds on College Green in Dublin on Saturday. Hide Caption 9 of 23 Photos: In pictures: Pope Francis visits Ireland Nuns wait for Pope Francis to arrive for the Festival of Families on Saturday. Hide Caption 10 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis leaves St. Mary's Pro-Cathedral in Dublin after meeting recently married couples, and couples preparing for the Sacrament of Marriage, as part of his visit to Ireland. Hide Caption 11 of 23 Photos: In pictures: Pope Francis visits Ireland Riverdance performs at the Festival of Families. Hide Caption 12 of 23 Photos: In pictures: Pope Francis visits Ireland Speaking in a hall in Dublin Castle on Saturday, Pope Francis addresses the sexual abuse scandal within the Catholic Church, saying, "the failure of ecclesiastical authorities -- bishops, religious superiors, priests and others -- adequately to address these appalling crimes has rightly given rise to outrage, and remains a source of pain and shame for the Catholic community. I myself share those sentiments." Hide Caption 13 of 23 Photos: In pictures: Pope Francis visits Ireland A journalist reacts inside the media center as Pope Francis arrives at Dublin Airport on Saturday. Hide Caption 14 of 23 Photos: In pictures: Pope Francis visits Ireland The Pope disembarks from the aircraft as he arrives in Dublin on Saturday. Hide Caption 15 of 23 Photos: In pictures: Pope Francis visits Ireland Priests await the arrival of Pope Francis at St. Mary's Pro-Cathedral. Hide Caption 16 of 23 Photos: In pictures: Pope Francis visits Ireland Protesters tie baby shoes to a post, signifying the children who died in mother and baby homes in Ireland, during a protest in Dublin ahead of the start of the Pope's visit to Ireland. Hide Caption 17 of 23 Photos: In pictures: Pope Francis visits Ireland The Pope is greeted by Archbishop Eamon Martin as he arrives at Dublin Airport on Saturday. Hide Caption 18 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis is flanked by Irish President Michael Higgins upon his arrival at the presidential residence in Dublin on Saturday. Hide Caption 19 of 23 Photos: In pictures: Pope Francis visits Ireland Members of the armed forces arrive before the meeting between the Pope and Irish President Michael Higgins at Aras an Uachtarain on Saturday. Hide Caption 20 of 23 Photos: In pictures: Pope Francis visits Ireland A crowd reacts to Pope Francis' arrival for the Festival of Families. Hide Caption 21 of 23 Photos: In pictures: Pope Francis visits Ireland Pope Francis waves to the crowd at Dublin Airport on Saturday. Hide Caption 22 of 23 Photos: In pictures: Pope Francis visits Ireland Rainbow flags and blue ribbons are tied to Ha'penny Bridge in Dublin to remember the victims of Catholic Church clerical sex abuse. Hide Caption 23 of 23

Cardinal Wuerl rejects allegations

Vigano also said Washington Cardinal Donald Wuerl was aware of reports of sexual abuse by his predecessor McCarrick.

"Cardinal Wuerl, well aware of the continuous abuses committed by Cardinal McCarrick and the sanctions imposed on him by Pope Benedict, transgressing the Pope's order also allowed him to reside at a seminary in Washington, D.C.," said Vigano.

"In doing so, he put other seminarians at risk," he added.

Edward McFadden, spokesperson for the archdiocese of Washington, disputed the notion that Wuerl ignored allegations about McCarrick.

"In spite of what Archbishop Vigano's memo claims, Cardinal Wuerl did not receive any documentation or information during his time in Washington regarding any actions taken against Archbishop McCarrick," he said.

The Archdiocese of Washington said: "Cardinal Wuerl has indicated that during his entire tenure as archbishop of Washington no one has come forward to say to him, 'Cardinal McCarrick abused me' or made any other like claim. The only ground for Cardinal Wuerl to challenge the ministry of Archbishop McCarrick would have been information from Archbishop Viganò or other communications from the Holy See."

"Perhaps the starting point for a serene and objective review of this testimony is the inclusion of Archbishop Viganò's tenure as Apostolic Nuncio to the United States in the mandate of the Apostolic Visitation already called for by Cardinal Daniel DiNardo, President of the UC," the statement said.

But the bishop of the Diocese of Tyler, Texas, told his parishioners he thinks the allegations are "credible."

"Let us be clear that they are still allegations, but as your shepherd, I find them to be credible," the Most Reverend Joseph E. Strickland wrote in a letter to members of the diocese.

Strickland's letter did not say why he believes the allegations are credible. CNN has reached out to his office for explanation.

The Archdiocese of Newark, New Jersey, and Cardinal Joseph W. Tobin issued a joint statement expressing "shock, sadness and consternation at the wide-ranging array of allegations published" by Vigano.

The statement said the allegations can't be "understood as contributing to the healing of survivors of sexual abuse."

"Together with Pope Francis, we are confident that scrutiny of the claims of the former nuncio will help to establish the truth," the statement said.

The Conference of Catholic Bishops' executive committee met Sunday and "reaffirmed the call for a prompt and thorough examination into how the grave moral failings of a brother bishop could have been tolerated for so long and proven no impediment to his advancement," DiNardo said in a statement.

DiNardo's statement said Vigano's letter "brings particular focus and urgency to this examination."

"The questions raised deserve answers that are conclusive and based on evidence. Without those answers, innocent men may be tainted by false accusation and the guilty may be left to repeat sins of the past," he said.

Vigano's statement comes at a delicate time for Pope Francis, who has just visited Ireland, where he grappled with the fallout of a Pennsylvania grand jury report into clerical sexual abuse spanning decades, while also meeting with survivors of Ireland's own sex abuse scandal.

Vigano has been a high Vatican official and lifelong diplomat. He's served in the Vatican Secretariat of State overseeing offices of nuncios, or papal ambassadors.

He has a reputation as a conservative. In his 11-page statement, he spoke at length about supposed "homosexual networks" in the Vatican.

During his time as the former US nuncio, Vigano aroused ire for setting up a secret meeting in Washington in 2015 between the Pope and Kim Davis , the Kentucky clerk who became a conservative Christian heroine for refusing to sign same-sex marriage certificates.

Even before the Davis affair, American gay rights groups complained about the nuncio.

The Human Rights Campaign wrote a letter to the Pope in 2015, urging him to rein in his nuncio and prevent Vigano from speaking at a rally against same-sex marriage in front of the Supreme Court.

CNN's senior Vatican analyst John Allen reported that he's "arguably undercut his credibility by not dealing with his own record on the abuse issue."

"According to a 2014 memo, first made public in 2016, Viganò as nuncio quashed an investigation -- going as far as demanding that evidence be destroyed -- into then-Archbishop John Nienstedt of St. Paul and Minneapolis, who was being investigated for misconduct with seminarians as well as cover-up of sexual abuse. In 2015, Nienstedt stepped down as head of the archdiocese," Allen reported in Crux

"By not at least trying to explain his actions in the Nienstedt case, Vigano left open some serious question marks."

The Pennsylvania report found that more than 1,000 minors had been sexually abused by more than 300 Catholic priests over seven decades.

In an unusually blunt letter released by the Vatican last week, the Pope directly referred to the Pennsylvania report and acknowledged the Catholic Church's failure to act, adding "we showed no care for the little ones; we abandoned them."

Visit to Ireland

On Saturday, the Pope again spoke in Dublin of his shame over the "appalling crimes" of historic child abuse in the Catholic Church and said outrage was justified, although he did not mention the Pennsylvania scandal specifically.

Meanwhile, Irish Prime Minister Leo Varadkar, who spoke ahead of the Pope on Saturday, did not skirt the current abuse revelations that have emerged in Pennsylvania.

"In recent weeks, we have all listened to heartbreaking stories from Pennsylvania of brutal crimes perpetrated by people within the Catholic Church, and then obscured to protect the institution at the expense of innocent victims," he said. "It is a story all too tragically familiar here in Ireland."

Pope Francis passes a protest banner after visiting St Mary's Pro-Cathedral in Dublin on Saturday.

Pope Francis concluded his 32-hour visit to Ireland with a Sunday Mass at Phoenix Park in Dublin, with hundreds of thousands of people braving wet and windy weather to attend. Thousands more gathered in the city center for protests against clerical sexual abuse.

"We ask forgiveness for the abuses in Ireland," said Pope Francis at the Mass, listing a litany of abuses including clerical sex crimes, a lack of compassion and action by church leaders and the separation of single mothers and children.

"We ask forgiveness for all the times that we, as the church, did not provide survivors of any kind of abuse compassion, to look for justice, and the truth, and concrete actions, so we ask forgiveness," Pope Francis said at the Mass.

Correction: An earlier version of this article incorrectly said that Carlo Maria Vigano is a former archbishop. He is still an archbishop.