The recently released grand jury report into sex abuse within the Catholic Church named Wuerl as someone who had allowed priests to continue their work despite allegations of abuse.
Viganò, a former Vatican ambassador to the USA, said he told the Pope about the allegations five years ago, but the pontiff did nothing about it. Viganò subsequently urged the Pope to resign.
Pope Francis will summon the presidents of every bishops conference to a meeting in February to discuss preventing clergy sex abuse and protecting children, his advisers revealed Wednesday.
Vigano, a former Vatican envoy to Washington, also called on the Pope to step down.
As Pope Francis sat down at the Vatican Thursday with a delegation of USA bishops and cardinals to discuss how to gain ground in the sexual abuse crisis engulfing the Catholic Church, fresh scandals emerged on both sides of the Atlantic.
"We shared with Pope Francis our situation in the United States - how the Body of Christ is lacerated by the evil of sexual abuse", the head of the delegation, Cardinal Daniel DiNardo of Galveston-Houston, said in a statement.
Vatican spokesman Greg Burke said DiNardo and O'Malley would meet with Francis on Thursday in the Apostolic Palace. An accusation surfaced against him during the 2012 trial of Philadelphia Monsignor William Lynn, who was convicted of child endangerment for covering up abuse, and served almost three years in prison before the Supreme Court vacated his conviction in 2016.
Google pulls Russian opposition leader's YouTube advert ahead of vote
The videos showed Mr Navalny calling for Russians to take part in protests on 9 September against raising the retirement age. Petersburg saw arguably the most robust response with riot police charging at protesters with batons.
Pope Francis accepted the resignation of a USA bishop Thursday and authorized an investigation into allegations he sexually harassed adults, adding awkward drama to an audience with US church leaders over the abuse and cover-up scandal roiling the Catholic Church.
In letter to priests today Cardinal Wuerl writes that he will travel again to Rome soon to meet with Pope Francis and discuss resignation.
The pope initially said he would not say a "single word" on the accusations and refused to even answer a question about when he first knew of McCarrick's behavior.
"The Holy Father Francis, after hearing the Council of Cardinals, has made a decision to convene a meeting with the presidents of the Episcopal Conferences of the Catholic Church on the theme of the 'protection of minors, '" the Vatican press office said in a statement.
Last month, Archbishop Carlo Maria Vigano sparked a firestorm when he accused Pope Francis of covering up sexual abuse allegations against an American cardinal.
Mr Di Nardo said he wants Francis to authorise a Vatican investigation into Theodore McCarrick, who was removed as cardinal in July after he was accused of groping a teenager.
A study commissioned by the German bishops' conference reports the sexual abuse of thousands of children by priests and religious in that country over a period of 70 years.