Cardinals have entered the Vatican’s Sistine Chapel, where they will begin voting to elect a new Pope.
The 115 cardinal-electors will be locked in the chapel after swearing an oath of secrecy.
They will vote four times daily until two-thirds can agree on a candidate.
The election was prompted by the surprise abdication of Benedict XVI. There is no clear frontrunner to take over from him as head of the Roman Catholic Church.
The 85-year-old Benedict stepped down last month saying he was no longer strong enough to lead the Church, which is beset by problems ranging from a worldwide scandal over child sex abuse to allegations of corruption at the Vatican bank.
His resignation and the recent damage to the Church’s reputation make the choice of the cardinal-electors especially hard to predict, the BBC’s James Robbins in Rome says.
They will weigh pressure for a powerful manager to reform the Vatican against calls for a new Pope able to inspire the faithful, our correspondent adds.
On Tuesday morning’s, the cardinals attended a “Mass for the Election of the Supreme Pontiff” in St Peter’s Basilica. They filed in wearing bright red vestments to the sound of Gregorian chanting.
In his homily, the Dean of the College of Cardinals, Cardinal Angelo Sodano, praised the “brilliant pontificate” of Pope Benedict and implored God to grant another “Good Shepherd” to lead the church.
He outlined the mission Catholics believe was given by Jesus Christ to St Peter – the first Pope – emphasising love and sacrifice, evangelisation and the unity of the church.
The BBC’s Michael Hirst in Rome says the speech was more measured in tone than the address given in 2005 by Cardinal Joseph Ratzinger before he became Pope Benedict, which featured a fiery attack on the “dictatorship of relativism”.
A few hundred people watched the Mass from St Peter’s Square on giant screens in thunderstorms and pouring rain.
At 16:30 local time (15:30 GMT), 115 cardinal-electors – all under 80, as those over 80 are excluded – entered the Sistine Chapel for the secret conclave to select Benedict’s successor, chanting the traditional Litany of the Saints.
Once they have taken an oath of secrecy, Msgr Guido Marini, papal master of ceremonies, will call out the words “Extra omnes” – “Everybody out” – and the chapel doors will be locked to outsiders.
Candidates named as contenders include Cardinal Angelo Scola of Milan, Brazil’s Odilo Scherer, and Cardinal Dolan himself – though he told one interviewer anyone who thought he was in with a chance might be “smoking marijuana”.
The smoke that will drift out of the chapel’s chimney early in the evening is likely to be black – meaning no Pope has been elected.
From Wednesday, two votes will be held each morning and afternoon – with ballots burned after each session – until one candidate attains a two-thirds majority (77 votes).
Then the smoke will be white, meaning the 266th bishop of Rome will have been chosen.
R.S