Francis said the 11-page text by Archbishop Carlo Maria Vigano "speaks for itself" and that he would not comment on it.
Francis was asked by a US reporter during an airborne press conference on Sunday if Mr Vigano's claims that the two discussed the Theodore McCarrick allegations in 2013 were true.
The pope was also asked about Mr Vigano's claims that McCarrick was already under sanction at the time, but that Francis rehabilitated him.
He said he had read Mr Vigano's document and trusted journalists to judge for themselves.
"It's an act of trust," he said. "I won't say a word about it."
The National Catholic Register and another conservative site, LifeSiteNews, published Mr Vigano's text on Sunday as the pope wrapped up a two-day visit to Ireland dominated by the clerical sex abuse scandal.
Mr Vigano, 77, a conservative whose hard-line anti-gay views are well known, urged the reformist pope to resign over what he called Francis' own culpability in covering up McCarrick's crimes.
Francis accepted McCarrick's resignation as cardinal last month, after a US church investigation determined that an accusation he had sexually abused a minor was credible.
Since then, another man has come forward to say McCarrick began molesting him starting when he was 11, and several former seminarians have said McCarrick abused and harassed them when they were in seminary.
The accusations have created a crisis of confidence in the US and Vatican hierarchy.
Coupled with the devastating allegations of sex abuse and cover-up in a recent Pennsylvania grand jury report - which found that 300 priests had abused more than 1,000 children over 70 years in six dioceses - the scandal has led to calls for heads to roll and for a full Vatican investigation into who knew what and when about McCarrick.
Mr Vigano apparently sought to answer some of those questions.
His letter identifies by name the Vatican cardinals and US archbishops who were informed about the McCarrick affair. He said documents backing up his version of events are in Vatican archives.
The Vatican's ambassador to the US from 2011 to 2016, Mr Vigano said his two immediate predecessors "did not fail" to inform the Holy See about accusations against McCarrick, starting in 2000.
Mr Vigano said he himself sent at least two memos on him.
He said Pope Benedict XVI eventually sanctioned McCarrick in 2009 or 2010 to a lifetime of penance and prayer, and to no longer celebrate Mass in public or travel.
He said Francis asked him about McCarrick when they met on June 23, 2013, at the Vatican's Santa Marta hotel where the pope lives, three months after Francis was elected pope.
Mr Vigano wrote that he told Francis: "Holy Father, I don't know if you know Cardinal McCarrick, but if you ask the Congregation of Bishops, there is a dossier this thick about him. He corrupted generations of seminarians and priests, and Pope Benedict ordered him to withdraw to a life of prayer and penance."
Soon thereafter, Mr Vigano wrote, he was surprised to find that McCarrick had started travelling on missions on behalf of the church, including to China.
McCarrick was also one of the Vatican's intermediaries in the US-Cuba talks in 2014.
Mr Vigano's claim that McCarrick had been ordered by Benedict to stay out of public ministry and retire to a lifetime of prayer is somewhat disputed, given that McCarrick enjoyed a fairly public retirement.
But Mr Vigano insisted the sanctions had been imposed, and said a former counsellor in the embassy at the time was "prepared to testify" about the "stormy" meeting when McCarrick was informed of them.
Barry Coburn, McCarrick's civil attorney, said the allegations in the Vigano letter are "serious".
"Archbishop McCarrick, like any other person, has a right to due process. He looks forward to invoking that right at the appropriate time," he said in a statement.
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