Cardinals resumed their voting in the secret conclave, having already failed to choose a new pope in the first round of voting on Wednesday evening.
Up to four rounds of voting can take place each full day of conclave, two in the morning and two in the afternoon.
Smoke is only expected up to twice a day, as ballots from two successive rounds are generally burned together if no pope is chosen in either round.
One prominent cardinal, who is not in the conclave as he is older than the age limit of 80 for participation, is reported to be hoping for a new pope by the evening.
According to reports in Italian media, Cardinal Giovanni Battista Re, the dean of the College of Cardinals, said on Thursday: “I hope that when I return to Rome this evening, I’ll find the white smoke already rising.”
The voting cardinals began their behind-closed-doors meeting shortly before 5pm UK time on Wednesday.
Pope Francis was elected after five ballots, and white smoke on the second day of that conclave confirmed the news to the world in 2013.
The voting ballots are burned with chemicals added in a special furnace to ensure the colour signals the correct result.
For black, to indicate no-one has been elected, the ballots are mixed with cartridges containing potassium perchlorate, anthracene – which is a component of coal tar – and sulfur.
For white to signal a new pontiff has been chosen, potassium chlorate, lactose and chloroform resin are added to the burning ballots.
It is expected a bell will also toll to mark the election of a new pope, to further confirm a choice has been made.
The cardinals in this conclave are gathering to elect the 267th pope and have, as is tradition, been cut off from communications with the outside world.
At a pre-conclave mass on Wednesday, they were reminded of the “choice of exceptional importance” they must make in electing the next pope.
A new pope requires a two-thirds majority in the voting.
Should the cardinals fail to reach an agreement on a candidate after three days of voting, they are entitled to a one-day break for prayer and free discussion.
Three UK cardinals are taking part in the conclave: Cardinal Vincent Nichols, Cardinal Timothy Radcliffe and Rome-based Cardinal Arthur Roche.
Cardinal Kevin Farrell, who is Irish-born, is considered an American cardinal, having ministered mainly in the US.
Cardinal Nichols had called on people to pray for himself and other cardinals as they embark on the secret voting process, adding that he feels “quite intimidated” knowing the world is watching to see who they choose.
The voting cardinals were urged to “invoke the help of the Holy Spirit” to help them elect a pope “whom the (Catholic) Church and humanity need at this difficult and complex turning point in history”.
Addressing them in St Peter’s Basilica on Wednesday, Cardinal Battista Re said: “To pray, by invoking the Holy Spirit, is the only right and proper attitude to take as the cardinal electors prepare to undertake an act of the highest human and ecclesial responsibility and to make a choice of exceptional importance.
“This is a human act for which every personal consideration must be set aside, keeping in mind and heart only the God of Jesus Christ and the good of the Church and of humanity.”
The pontiff – believed to be someone called to be the successor to St Peter, who was the first pope – will need to be a person who can “awaken the consciences of all and the moral and spiritual energies in today’s society, characterised by great technological progress but which tends to forget God”, Cardinal Battista Re added.
This conclave is thought to be one of the most diverse of any meeting of cardinals, representing some 70 countries and hailing from places such as Mongolia, Sweden and Tonga, which had not had a cardinal before.
Pope Francis had appointed some 108 of the 133 cardinals who will choose his successor.
Dubbed the people’s pope, he was a popular pontiff whose death on Easter Monday sparked tributes from leaders across the world and whose funeral drew hundreds of thousands of mourners.
