ROME — For the second time in three days, Pope Francis on Monday accepted the resignation of a powerful prelate — this time, an Australian archbishop — in a sexual abuse scandal, as the pontiff tries to send the message that high officials no longer enjoy near-immunity from consequences within the church when it comes to sexual misconduct.

The archbishop, Philip Edward Wilson of Adelaide, had resisted intense pressure in Australia to resign, despite his criminal conviction for covering up for sexual abuse by a priest. Two months after being found guilty, he submitted his resignation on July 20, though it was not made public until the pope accepted it on Monday.

Two days earlier, on Saturday, Francis accepted the resignation from the College of Cardinals of Cardinal Theodore E. McCarrick, a former archbishop of Washington and of Newark — the first time in memory that a cardinal stepped down over sexual abuse allegations against him.

Early this year, the pope drew criticism for speaking in defense of a Chilean bishop caught up in another abuse case, and many advocates against clerical sex abuse said that Francis seemed to have a blind spot on the issue.