Cardinals of the Roman Catholic Church have celebrated a special Mass at the Vatican at the beginning of a process to choose the new pontiff.
"Give to us a pope who is acceptable to you," Cardinal Joseph Ratzinger, considered to be a front-runner, said.
In a homily, he spoke of the need to preserve the Church's traditional Catholic tenets against modern trends.
Later on Monday, 115 cardinals eligible to vote will enter the Sistine Chapel for the highly secretive ballot.
Cut off from the world, they will hold up to four ballots a day until a successor to John Paul II is chosen.
The cardinals will decide on whether to hold the first vote as early as Monday evening - or to continue their reflection and discussion before voting on Tuesday morning.
Pope John Paul died on 2 April and was buried a week later.
CONCLAVE DAILY SCHEDULE
0730: Cardinals celebrate Mass in hotel
0900: Morning voting starts
1600: Afternoon voting starts
1200 & 1900: Smoke comes out
White smoke appears earlier if pope elected
New pope appears on the balcony 45 minutes later
All times local
Strict security measures have been imposed to ensure secrecy is kept.
Parts of the Vatican have been sealed off, and all staff who will come into contact with the cardinals have taken a vow of silence.
Mobile phones, newspapers and television are banned, and the Sistine Chapel has been swept to check for bugging devices.
The cardinals taking part in the conclave, as it is known, will head for the Sistine Chapel at 1630 (1430 GMT) in the full view of television cameras.
Once inside the chapel, they will swear the oath of secrecy, pledging also to observe the Apostolic Constitution during the election process.
Many of the cardinals checked into the Domus Sanctae Marthae hotel, nestled within the city-state's walls, on Sunday.
Pope John Paul II ordered the hotel to be built so that the cardinals could enjoy some level of comfort during the intense voting process to elect his successor.
Pope John Paul II was elected after eight ballots. This time, the cardinals may come to a decision within days, but previous conclaves have been known to go on for months.
The new pope is elected with a two-thirds majority, unless, after 34 ballots, cardinals decide to change the rules in favour of a simple majority.
Conservative or liberal?
Some experts predict a hard struggle between liberals and hardline conservatives, leading to a long conclave and perhaps a surprise result.
Despite the high levels of secrecy, some indications of feelings inside the conclave have emerged from apparent leaks by Italian cardinals to the Italian press.
115 take part
Must be aged under 80
Come from 52 countries
Largest number, 58, are from Europe
Individual countries with most are Italy (20) and US (11)
In a sermon on Saturday, German cardinal Walter Kasper said the Church needed a pope with strong pastoral skills.
The BBC's David Willey in Rome says this was a veiled attack on Cardinal Ratzinger - a German conservative who has spent the past 20 years at the Vatican.
The only real clue about what is going on inside the Sistine Chapel is the smoke that emerges from a specially installed chimney made from burning the ballot papers.
Chemicals are added to colour the smoke - black smoke signals failure, while white smoke means a new pope has been chosen.
This year, the white smoke will be accompanied by the ringing of the bells of St Peter's Basilica.
Full details of the actual vote will not be published for 100 years.