The election came on the first full day of voting by the 133 cardinal electors, who secluded themselves behind the Vatican's medieval walls on Wednesday afternoon.
Italian Cardinal Pietro Parolin, who served as the Vatican's number two under Francis, and Filipino Cardinal Luis Antonio Tagle are considered the front-runners.
Trump told reporters on Monday that the pope image was posted as a joke on his Truth Social account, which was then reposted by the White House across social media.
Prime Minister Benjamin Netanyahu expressed his condolences to the Catholic world for Pope Francis' death three days after pontiff passed away.
In the wake of Pope Francis’ death on Monday, Catholic cardinals from across the world will gather for a conclave in the Vatican’s Sistine Chapel to elect the next pope.
Pope Francis, who passed away on Monday at the age of 88, was an "alien presence" at the Vatican, bringing about a revolution of modesty and simplicity within the Catholic Church.
The following rituals mark the end of one papacy and the start of the next.
"The global Catholic community bids farewell to a leader who recognised the burning issues of our day and called attention to them," Dutch Prime Minister Dick Schoof said.
Pope Francis suggested the global community study whether Israel's military campaign in Gaza constitutes a genocide of the Palestinian people.
King Charles and Queen Camilla had been due to make a formal state visit to the Vatican, but postponed their plans after doctors prescribed Francis two months of rest.
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