The pair are among the most contentious Roman Catholic figures of the 20th century.
The bishops sought an inquiry into the Vatican’s handling of a former cardinal accused of sexual misconduct, but the meeting’s outcome was not disclosed.
Cardinal Daniel DiNardo of Texas was accused of covering up abuse by a priest as he met with the pope to discuss reform in his role as president of the U.S. Conference of Catholic Bishops
The Feb. 21-24 meeting at the Vatican is believed to be the first of its kind.
Some Catholics have criticized him for what they describe as an insufficient response to the sexual abuse crisis.
In a new statement, the allies appeared to concede a central claim of Archbishop Carlo Maria Viganò, who has called on the pope to step down.