“Mere words at this point deepen the insult and the pain,” she wrote in a statement to the news media.

When Francis assumed the papacy from Benedict in 2013 he was a charismatic leader whose very utterances were seen as action. But the frequency of abuse cases and the church’s inability to offer a comprehensive reckoning have tried the patience of even his supporters and have begun to overwhelm the pope’s popularity and moral authority.

The scale of the problem, especially after the new round of revelations, also seems to dwarf the pope’s recent strengthening of his policy of addressing sex abuse in specific countries.

Some advocates for abuse victims have called for a worldwide zero tolerance policy, which would take away bishops’ leeway in how to deal with convicted and plausibly accused priests. Activists also want a standardized system for punishing bishops and other religious superiors who allowed child sex abuse to continue under their watch. They want the church to open its archives willingly, without the threat of subpoena.

Prosecutors in various countries are taking matters into their own hands and putting clerics on trial, Ms. Doyle said. “If the pope doesn’t get his house in order, the civil authorities will do it for him,” she said.

In 2010, Benedict wrote a letter to Ireland’s Catholics when the abuse scandal came to the fore there. And earlier this year, after the missteps in his handling of the Chilean scandal — including defending a bishop from the “calumny” of victims — Francis wrote to Catholics in Chile.

But Monday’s letter was different, the Vatican said. “This is about Ireland, this is about the United States, and this is about Chile. But not only,” Greg Burke, the director of the Holy See Press Office said in an audio statement. “Pope Francis has written to the people of God and that means everyone.”