The sessions focused on a new Apostolic constitution that, among other things, allows lay people to head important Vatican offices, envisioning greater decision-making roles for them, including women.

But since the church has closed the door to women in the priesthood, the most prestigious, and ultimately most powerful roles — including that of a pontiff — remain the realm of men.

The reforms also lend more institutional weight to efforts to fight clerical sex abuse. The document, made public earlier this year, replaced the constitution written by St. John Paul II in 1988.

Francis on Saturday raised 20 churchmen to the rank of cardinal, including 16 younger than 80 and thus eligible to vote in a conclave to elect his successor, when the time comes.

Until Pope Benedict XVI resigned in 2013, the first pontiff in almost 600 years to do so, conclaves in recent centuries had followed the death of popes. Francis, who is 85, has said that resignation can be a valid option for pontiffs who can’t adequately carry out their role as leader of the world’s more than 1.3 billion Catholics.

But he has brushed off talk that he is contemplating stepping down soon despite health problems, including a bad knee that necessitates frequent wheelchair use.

In his homily at a Mass in St. Peter’s Basilica to close out the meetings, Francis offered no details about this week’s discussions. But he exhorted the cardinals, known as the “princes of the church,” to be on guard against the “cancer, the woodworm, of worldly spirituality.”

While in Rome these days, cardinals from around the world could size each other up. Encounters, including informal ones, allow them to see who might have the potential to become a future pope as well as to ponder possible alliances among geographical groupings or among like-minded churchmen from more conservative or more progressive factions.

The Vatican said among themes discussed were the role of lay persons, financial transparency, the managerial structure of the Vatican bureaucracy as well as how to “announce the Gospel in an epoch like the current one.”

Francis has worked to reform the Holy See’s finances, including its multimillion-dollar investments, one of which is at the heart of a trial underway at the Holy See and involving, among others, a Vatican cardinal.

Francis has tried to make the church more inviting to those who might feel unwelcome, including LGBTQ Catholics, or undervalued, including women.

On Monday, a half-dozen female activists protested as cardinals, with their iconic red headgear, flocked to the meeting on Vatican grounds. The women held up red parasols with slogans reading, “Sexism is a Cardinal Sin.” Other slogans were: “It’s reigning men” and “Ordain Women.”

One protester, Miriam Duignan, lamented that the cardinals were “going to talk about the future of the church without half of the church.”