The Catholic Church’s pushback Sunday against Archbishop Carlo Maria Viganò, author of the bombshell accusation of a sex abuse cover-up against Pope Francis, has ensnared a key figure in the U.S. culture wars: Kim Davis.

The Rev. Federico Lombardi and his English-language assistant, the Rev. Thomas Rosica, issued a joint statement late Sunday disputing Viganò’s claims about the encounter he organized with Davis during Pope Francis’ September 2015 visit to the United States. Davis, of Rowan County, Kentucky, made headlines around the world after she cited her own faith to deny marriage licenses to gay couples.

The Vatican had sought to downplay the encounter after conservatives presented it as a papal stamp of approval for Davis.

However, Viganò, the papal ambassador — or nuncio — to Washington between 2011 and 2016, said in a statement last Thursday that Francis knew well who Davis was, and that the Vatican approved the meeting in advance.

Francis was so enraged that Davis’ supporters had leaked word of the meeting that the Vatican subsequently insisted he only held one private audience while there: with one of his former students, a gay man and his partner, as Fox News previously reported.

In the joint statement Sunday, Rosica transcribed what he said were handwritten notes from a meeting he and Lombardi had with Viganò after the Davis encounter. In those notes, Rosica quoted Viganò as telling them that the pope had actually chastised him for "deceiving" him with the Davis meeting, and for having withheld the fact that Davis had been married four times.

In his part of the joint statement, Lombardi said Viganò initiated the Davis meeting, should have known about the furor that it would cause, and that even though Vatican officials approved of it, they were not sufficiently informed about the significance such a meeting would take on.

The timing of Viganò’s accusations has been seen by the progressive pope’s supporters as a deliberate attempt by more conservative factions to undermine his tenure, which has seen him reach out to homosexuals and divorced parishioners.

In a damning 11-page letter released to ultra-conservative media in Europe last Sunday, during the pope’s trip to Ireland, Viganò called on the pope to resign, accusing him of being among Church hierarchy who knew — and did little or nothing — about rumored indiscretions by ex-Cardinal Theodore McCarrick.

In fact, Viganò asserted, McCarrick was rehabilitated from sanctions imposed by Pope Benedict XVI, promoted and made part of high-profile Vatican events even as rumors about him swirled.

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.

Francis accepted McCarrick’s resignation as cardinal last month, after the U.S. 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 U.S. and Vatican hierarchy, because it was apparently an open secret that McCarrick regularly invited seminarians to his New Jersey beach house, and into his bed.

Fox News’ Elizabeth Llorente, Samuel Chamberlain and The Associated Press contributed to this report.