The Vatican's ambassador to the US from 2011 to 2016, Vigano said his two immediate predecessors "did not fail" to inform the Holy See about accusations against McCarrick, starting in 2000.
But he claims he was surprised to find McCarrick back on Church missions after Francis became pope in 2013, although the claim that Benedict sanctioned him is disputed.
"You have sufficient journalistic capacity to draw conclusions", he said.
Archbishop Carlo Maria Vigano, a former Vatican envoy to the United States, said he had told Francis of the claims against prominent U.S. cardinal Theodore McCarrick in 2013.
Vigano writes that he told Francis about the allegations: "HolyFather, I don't know if you know Cardinal McCarrick, but if you ask the Congregation for Bishops there is a dossier this thick about him".
"I do not know when Pope Benedict took these measures against McCarrick, whether in 2009 or 2010, because in the meantime I had been transferred to the Governorate of Vatican City State, just as I do not know who was responsible for this incredible delay", he said.
Pope Francis has refused to respond to claims by a former Vatican diplomat, who has called for him to resign.
"He (Pope Francis) knew from at least June 23, 2013 that McCarrick was a serial predator", wrote Vigano", adding "he knew that he was a corrupt man, he covered for him to the bitter end.
Archbishop Carlo Maria Viganó, for five years the papal nuncio for the United States, on Saturday released a damning 11-page letter claiming that a Vatican cabal has consistently downplayed and even hidden abuse charges against high church figures.
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"I repeated them to Cardinal McCarrick at my first meeting with him at the nunciature".
This allegedly occurred in 2013, soon after he was elected pope.
"Make no mistake. This is a coordinated attack on Pope Francis", said an editorial article on the website of the progressive National Catholic Reporter weekly.
"Regarding Cardinal Sean O'Malley, I would simply say that his latest statements on the McCarrick case are disconcerting, and have totally obscured his transparency and credibility", Vigano wrote.
88-year-old McCarrick resigned last month in disgrace and was stripped of his title after allegations that he had abused a minor almost 50 years ago and also forced adult male seminarians to share his bed.
The Irish Catholic Church has been rocked by revelations of paedophile priests, sexual abuse in Catholic-run orphanages, and the exploitation of women in mother-and-baby homes.
McCarrick, now 88, resigned in disgrace in July.
Barry Coburn, McCarrick's civil attorney, said the allegations in the Vigano letter are "serious".
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.
"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.