The Diocese of Brooklyn said it was “appalled" by the video, which was shot at Our Lady of Mount Carmel-Annunciation Parish in Williamsburg.
Bishop Joseph Strickland had said in interviews he would not leave his post voluntarily.
Pope Francis responded to questions from five conservative cardinals in a way that marks a reversal from the Vatican's current official position.
A judge ruled Wednesday that former Cardinal Theodore McCarrick, who is 93 and has dementia, is not competent to stand trial.
Pope Francis, who embraces tackling issues like climate change and poverty, said a correct understanding of Catholic doctrine allows for change over time.
The Irish singer who once famously tore up a photo of the pope on live television has died at age 56.
Illinois' attorney general said the results of a sweeping investigation reveal that 451 Catholic clergy sexually abused nearly 2,000 children since 1950.
More than 150 Catholic priests and others associated with the Archdiocese of Baltimore sexually abused more than 600 children over the past 80 years.
Francis' comments are the first uttered by a pope about such laws, but are consistent with his overall approach to the LGBTQ community.
The cardinal was convicted of molesting two choirboys in the 1990s, but Australia's highest court overturned that verdict two years later.