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The Vatican meetings will set the date for the start of the conclave this month and help identify candidates among the cardinals to be the next leader of the world's 1.2 billion Catholics.
"We're going to take as much time as we need to think about what sort of pope the Church needs now," French cardinal Andre Vingt-Trois told reporters as he arrived for today's meetings.
"I'd be keen to have a polyglot, a man of faith, a man of dialogue... The new pope will certainly have to confront problems within the Curia," the government of the Catholic Church, he said.
Benedict's eight-year pontificate was often overshadowed by Vatican intrigue and scandals in Europe and North America over sexual abuse by paedophile priests going back decades and the cover-up of those crimes by senior prelates.
A total of 115 "cardinal electors" -- cardinals aged under 80 -- are expected at the conclave after Britain's Keith O'Brien opted out and an Indonesian cardinal said he was too sick to attend.
O'Brien had already recused himself from the conclave and resigned as head of the Scottish church after allegations of misconduct surfaced.
"My sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal," he said in a statement yesterday.
The field for next pope remains wide open after Benedict became only the second pontiff to step down by choice in the Church's 2,000-year history and the first to do so since the Middle Ages.
The Vatican says it expects a new pope by Easter, the most important date in the Christian calender which this year falls on March 31.
Vatican observers say there are possible candidates from every corner of the world and from both progressive and traditionalist wings of the Church, which is facing challenges on many levels.
Church leaders are also concerned about issues like priestly celibacy, treatment of gays, attitudes towards divorcees, the Catholic stance on contraception as well as inter-religious dialogue, particularly with Islam.
Benedict's effort to revive faith amid rising secularism is also seen as crucial.
"The key themes the Church will have to face are inter-religious issues and poverty and the crisis we're now seeing throughout Europe will spread," Vingt-Trois said today.
No date has yet been set for the election of the Church's 266th pope, although Italian media have mentioned next Monday, March 11 as a possibility.
The dean of the college of cardinals, Angelo Sodano, has said the start date will not be set until all the "cardinal electors" are in Rome.
The profile of an ideal candidate for pope is beginning to come into focus as cardinals have their say -- many would prefer a relatively youthful, pastoral figure who can help foster spiritual renewal, particularly among young people.
"When John Paul II died in 2005, everyone had been thinking about a successor for months and the conclave was short," a retired cardinal told AFP.
"This time the unprecedented move of a pope resigning has upset all the calculations," he said, adding that he believed a "bold decision" like the unexpected election of Poland's Karol Wojtyla in 1978 is a distinct possibility.
