The conclave will start behind the closed, wooden doors of the Sistine Chapel on Wednesday afternoon, with all cardinals aged under 80 entitled to take part to choose a successor to Francis, who died last month.
Some cardinals are looking for a new Pope who will continue with Francis' push for a more transparent, welcoming Church while others are seeking retrenchment to more traditional roots that put a premium on doctrine.
Conclaves are often spread out over several days, with multiple votes held before a contender wins the necessary three-quarters majority to become pope.
The world's Catholic cardinals have been meeting on a near daily basis since the day after Francis' death on April 21 to discuss the state of the 1.4-billion-member Church, with the numbers of participating clerics gradually swelling.
The Vatican said 180 cardinals, including 132 electors, took part in a meeting on Monday morning.
The 133rd elector is also in Rome but did not take part in the discussions.
Two cardinals, one from Spain and one from Kenya, will not be joining the conclave for health reasons, the Vatican said.
Among the questions addressed on Monday were "strong concern" about divisions within the Church, said the Vatican spokesman - a possible reference to splits over Francis' decision to allow blessings for same-sex partners and to open discussion about the role of women in the Church.
Cardinals also talked about the profile of a future Pope - "a figure who must be present, close, capable of being a bridge and a guide ... a shepherd close to the real life of the people," the spokesman said.
While there are a few cardinals seen as potential front-runners to succeed Francis - two often mentioned are Italian Cardinal Pietro Parolin and Filipino Cardinal Luis Antonio Tagle - many of the voting clerics have not made up their minds.
"My list is changing, and I think it will continue to change over the next few days," UK Cardinal Vincent Nichols, participating in his first conclave, told Reuters.
"It's a process which for me is far from concluded, far from concluded."
The cardinals will hold a second session of talks on Monday afternoon, with a final round expected on Tuesday.
Two Vatican guest houses will house the cardinals during the conclave, when they will be barred from contact with the outside world.
Progressive German Cardinal Walter Kasper, who is 92 and cannot take part in the vote, said he was sure the electors would choose someone to pursue Francis' agenda.
"I believe that there is a very clear expectation. People want a Pope to follow Francis. A pastor who knows the language of the heart, who does not close himself in palaces," Kasper told La Stampa newspaper.
"Of course, there are also cardinals who hope for a change of direction with respect to Francis. But my impression ... is that the majority of cardinals are in favour of continuity."
