NEW: Not all cardinal-electors have to be present for the conclave date to be set 110 of the 115 cardinal-electors have now arrived in Rome, says Vatican spokesman The Sistine Chapel closes to the public ahead of the conclave Rome (CNN) -- Catholic cardinals have met for a second day Tuesday at the Vatican, but have not yet set a timetable for selecting a new pope. A total of 110 out of the 115 cardinal-electors, those younger than 80 who are eligible to elect the pope, are now in Rome, Vatican spokesman the Rev. Federico Lombardi said Tuesday. The five cardinal-electors who have not yet arrived have been in touch with the College of Cardinals, and the Vatican knows when they are coming, he said. He did not say when that would be, however, or give reasons for their delayed arrival. No date has yet been proposed for the conclave to select Pope Benedict XVI's successor, said Lombardi. It is not necessary for all the cardinal-electors to be present for the conclave date to be set, he said, but they do have to be given time to get there. Another Vatican spokesman, the Rev. Thomas Rosica, said: "There is no desire to rush things but to take this time for discernment and reflection, and that's been evident in the meetings thus far." The famous Sistine Chapel, where the secretive conclave takes place, was closed to the public at lunchtime Tuesday for preparations and will remain so until further notice, the official Vatican Museums website said. Those cardinals already in Rome met twice Monday, in the morning and in the evening, as they began a series of meetings known as General Congregations. The group decided that congregations on Tuesday and Wednesday would take place in the morning only. The General Congregations are a key step before the conclave. Cardinals who want to speak in the General Congregations sign up to do so, and can speak as long as they want on any topic they want, Lombardi said. So far, 33 cardinals have spoken. There are 148 in the congregations as of Tuesday morning, he said. The cardinals also talked about the kind of pope they want to see at the head of the world's 1.2 billion Roman Catholics. Representatives of a support group for abuse victims, Survivors Network of those Abused by Priests, or SNAP, called Monday for the cardinals to elect a new pope who is not a Vatican insider. The group also called for some of the older cardinals to absent themselves from the General Congregations, arguing that some have been accused of complicity in protecting priests accused of sexually abusing children. "Their peers should push them to stay home, or they should do so voluntarily, the group feels, for the sake of the church and to avoid heaping more pain on wounded victims and betrayed Catholics," a statement on SNAP's website said. One of Italy's anti-clerical abuse networks, L'Abuso, petitioned senior Vatican Cardinal Tarcisio Bertone on Monday not to allow the participation of an Italian cardinal it alleges helped protect priests who molested minors in the past. Wounded 'hearts and minds' The Vatican refused to answer questions Monday about whether it would discipline O'Brien. "It looks as if the incidence of abuse is practically zero right now as far as we can tell, but they are still the victims, and the wound therefore is deep in their hearts and minds very often," Cardinal Francis George, archbishop of Chicago, told reporters in Rome. As long as it's with them, it's with all of us. And that will last for a long time, so the next pope has to be aware of this. More than 5,000 journalists are now accredited for the papal conclave, Lombardi said Tuesday. They cover 24 languages, he said. CNN's Richard Allen Green and Hada Messia reported from Rome and Laura Smith-Spark wrote and reported in London.