St. Peter's Square, Vatican
A few nuns walk through a nearly empty St. Peter's Square in the Vatican Saturday, March 2, 2013. Reuters

Roman Catholic cardinals, fearing that Pope Benedict XVI’s resignation has weakened his office, will ask the next pope to pledge in his inaugural address that he will serve until his death, European media report.

According to the Sunday Times of London, an unnamed cardinal told the Corriere della Sera newspaper of Milan that the rule that a pope has the right to resign of his own free will can’t be changed, "but for the future we need to safeguard the freedom of the church from external influences." The fear is that a future pope could be pressured into stepping down.

On Friday, Benedict said he was "not abandoning the Cross, I am staying in a new way," the Times reported. This was seen as a response to Polish Cardinal Stanislaw Dziwisz, a former personal secretary to his predecessor John Paul II, who said of his resignation: "One doesn't step down from the Cross."

Benedict has agreed that three cardinals who investigated the "Vatileaks" scandal would give their peers details of their secret report, which he received in December. Some have speculated that the report is so damaging it precipitated his resignation. The Vatican has denied allegations that it reveals a gay sex scandal in the Vatican that has left top clerics open to blackmail.

Although the conclave has not begun, the cardinals have already begun meeting in small groups to discuss their choice of successor. Observers noted that as he said farewell to the cardinals on Friday, Benedict spent the longest time with Angelo Scola of Milan, Christoph Schonborn of Vienna and Luis Antonio Tagle of Manila, all seen as possible successors.

"Among you there is the future pope, to whom today I declare my unconditional reverence and obedience," Benedict told all the cardinals.

The College of Cardinals will meet Monday for the first time since the pope's resignation.

Officially, the princes of the church will gather every day in what are called general congregations to deal with important ecclesiastical business -- setting a start date for the conclave, receiving reports on the state of church affairs around the world.

"This is the chance, especially for the cardinals out of Rome who don't travel a lot, to get to know the other cardinals better," the Rev. Thomas Reese, Vatican analyst for the National Catholic Reporter, told NBC News.

In these informal meetings, the cardinals will get acquainted and size each other up for “papability.”

"You're not going to do this in McDonald's," Reese said. "This is where the Roman cardinals have the home-court advantage because they have apartments, they probably have a cook, they know a restaurant with a private room where they can have three or four people for dinner."

Meanwhile, the church marked its first Sunday in nearly eight years without a papal blessing.

The windows of the papal apartments overlooking St. Peter's Square were shut, which is normally the case only when a pope is outside Rome and delivers the Sunday blessing elsewhere, Reuters reported.

There was no papal blessing of any kind, the first time the church has been in such a state of limbo since Sunday, April 3, 2005, the day after Pope John Paul died.

"It's strange, very strange to come to Rome to St. Peter's Square and not to hear the Angelus (Sunday blessing) of the pope, especially because the pope is still alive - it's a unique situation that we are living through," Fabio Ferrara, who was one of the few people in the square at noon, told Reuters.

"We have been praying a lot, it's sad, it is very, very sad, we feel like orphans," said Sister Agnese Carreddu, an Italian nun in the square.

Catholics at Sunday masses throughout the world did not hear the customary prayer for "our pope, Benedict." It will be omitted from every mass until there is a new pope.