ROME — Retaliating against a remarkable campaign from within the church to force the ouster of Pope Francis, the Vatican’s former spokesman issued a statement on Sunday night questioning the credibility of an archbishop who has accused Francis of covering up sexual misconduct.

But in seeking to defend the pope against the latest allegations, which relate not to abuse but to the pope’s own credibility, the former spokesman, the Rev. Federico Lombardi, seemed to confirm a key part of the archbishop’s claims. And the defense also offered a portrait of the pope and his top advisers as having been politically naïve.

In a letter released Friday, the archbishop, Carlo Maria Viganò, challenged the notion, put forward by Vatican officials and the pope, that he had ambushed Francis in 2015 by setting up a private meeting at the Vatican’s Washington embassy with Kim Davis, the Kentucky county clerk who became a conservative celebrity by refusing to issue marriage licenses to same-sex couples.

Archbishop Viganò said in the letter that he had fully briefed Francis and his top advisers, all of whom he named, about Ms. Davis and her “conscientious objection” to promoting same-sex marriage. He received approval from them all, he said.