Archbishop Carlo Maria Vigano, a former Vatican envoy to the United States, said he had told Francis of the claims against prominent US cardinal Theodore McCarrick in 2013.
But rather than punish McCarrick, who was forced to resign last month, Vigano said Francis had lifted sanctions imposed on him by his predecessor Pope Benedict XVI.
"Corruption has reached the very top of the Church's hierarchy," Vigano said in an eleven-page letter published on Saturday in the National Catholic Register and several conservative US Catholic publications.
But the pope refused to address the allegation on Sunday.
"I will not say a word about that. I think that the communique speaks for itself," Francis said on his plane as he flew back from Dublin to Rome.
The timing of the letter's release -- right in the middle of Francis's landmark trip to Ireland -- has raised speculation of a campaign by conservatives in the Church against the liberal pontiff.
Francis told journalists to "read the communique attentively and make your own judgement," referring to Vigano's letter.
"You have sufficient journalistic capacity to draw conclusions," he went on.
"When a little time has passed and you have the conclusions perhaps I will talk..," he added.
- 'Serial predator' -
Bishop Vigano, 77, who was a papal nuncio in Washington between 2011 and 2016, said that Benedict XVI imposed canonical sanctions against McCarrick in the late 2000s.
McCarrick was forced to leave his seminary and live a life of penance after former Vatican ambassadors in Washington, now dead, reported him for "gravely immoral" behaviour with seminarians and priests.
Vigano claimed Francis asked him about McCarrick when he took office in June 2013, but that the pope ignored his warnings.
He said the pope "knew from at least June 23, 2013, that McCarrick was a serial predator," adding that "he knew that he was a corrupt man, he covered for him to the bitter end".
The pope accepted the resignation of McCarrick, now 88, in July, making him just the second cardinal ever to lose his status.
In Ireland on Sunday the pope "begged for God's forgiveness" for past clerical abuse scandals, which have badly damaged the image of the Church in the Catholic stronghold.
He spoke of the "open wound" of clerical abuse, demanding "firm and decisive" measures to find "truth and justice" before saying mass to tens of thousands of flag-waving worshippers.
His trip was also met with protests, with about 5,000 abuse victims and supporters attending a "Stand for Truth" rally in the capital Dublin, while another "Nope to the Pope" demonstration called for gay and transgender recognition.
It was the first papal trip to Ireland since John Paul II spoke in front of 1.5 million people during a visit in 1979.
The pope went to Ireland to close the 2018 World Meeting of Families -- a global Catholic gathering that addressed issues including the treatment of gay people in the Church.
On the plane back to Rome after the two-day trip, the pope recommended parents seek psychiatric help for children who show homosexual tendencies.
"When it shows itself from childhood, there is a lot that can be done through psychiatry, to see how things are. It is something else if it shows itself after 20 years," he said.
- 'Stain' on the Church -
Irish Prime Minister Leo Varadkar on Saturday urged the pope to take action against abuses and ensure justice for abuse victims worldwide.
"Holy Father, I ask that you use your office and influence to ensure that this is done here in Ireland and across the world," he said, calling the scandals a "stain" on the Church and state.
The pope met eight abuse victims on Saturday, including a woman assaulted by a priest when she was in hospital aged 13.
On the plane to Rome, Francis said he "suffered a lot" at the meeting.
The Church's standing has been badly dented by the abuse scandals and the Irish have shed traditional Catholic mores, voting earlier this year to legalise abortion after approving same-sex marriage in 2015.
Multiple probes in Ireland have found Church leaders protected hundreds of predatory priests and former Irish president Mary McAleese revealed this month that the Vatican had sought to keep Church documents inaccessible to government investigators.
The abuse scandals in Ireland are part of a worldwide crisis for the Vatican.
A devastating report earlier this month accused more than 300 priests in the US state of Pennsylvania of abusing more than 1,000 children since the 1950s.
