Francis was speaking to reporters aboard the papal plane as he made the journey from Dublin back to the Vatican.
He said he would “not say one word” on the 11-page document, in which a former Vatican official, Archbishop Carlo Maria Vigano, says Francis should resign.
The pontiff said journalists should read the document carefully and decide for themselves about its credibility.
He said: “I read that statement this morning. I read it and I will say sincerely that I must say this, to you – the reporter – and all of you who are interested: read the document carefully and judge it for yourselves.
“I will not say one word on this. I think the statement speaks for itself and you have sufficient journalistic capacity to reach your own conclusions.”
Archbishop Carlo Maria Vigano, who made the accusations, says the Pope knew about sex abuse allegations concerning prominent US cardinal Theodore McCarrick for years.
Mr Vigano put together the accusatory document before delivering a bombshell statement to conservative Roman Catholic media outlets during the Pope’s visit to Ireland.
In an unprecedented move by a Church insider against the Pope, Mr Vigano accused the current and previous Vatican of covering up the case of former Cardinal Theodore McCarrick, the retired archbishop of Washington DC.
88-year-old McCarrick resigned last month in disgrace and was stripped of his title after allegations that he had abused a minor nearly 50 years ago and also forced adult male seminarians to share his bed.
According to Mr Vigano, McCarrick’s misconduct was known in the Catholic hierarchy for years, and former Pope Benedict XVI ordered him to seclusion for prayer and penance nearly a decade ago.
Pope Francis allegedly removed those sanctions and made McCarrick “his trusted counsellor” despite knowing him to be a “serial predator”.
Mr Vigano claims Francis knew former Cardinal McCarrick had “corrupted generations of seminarians and priests.”
In June 2013, the former Archbishop contends, Pope Francis asked his assessment of McCarrick during a private audience.
According to Mr Vigano, McCarrick’s misconduct was known in the Catholic hierarchy for years, and former Pope Benedict XVI ordered him to seclusion for prayer and penance nearly a decade ago.
Pope Francis allegedly removed those sanctions and made McCarrick “his trusted counsellor” despite knowing him to be a “serial predator”.
Mr Vigano claims Francis knew former Cardinal McCarrick had “corrupted generations of seminarians and priests.”
In June 2013, the former Archbishop contends, Pope Francis asked his assessment of McCarrick during a private audience.
Mr Vigano alleges that the Pope replied: “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.”
Former Archbishop Vigano writes he now believes Francis was being “deceitful,” gauging whether Mr Vigano “was an ally of McCarrick or not.”
Mr Vigano is a conservative who has clashed with the more liberal Francis.
His letter also accuses a number of other high-ranking ecclesial figures, some of whom have also had conflicts with Mr Vigano in the past.