The Vatican released no information about what the two popes discussed, The New York Times reported. But officials said that when Pope emeritus Benedict suggested Francis take the place of honor during prayer, Francis instead said they should pray as "brothers."
The lunch was the first meeting between two popes in centuries. Benedict is the first pope in more than 600 years to retire instead of dying in office.
Benedict, now known as the pope emeritus, has lived at the papal summer retreat south of Rome since stepping down last month. He is expected to stay there until accommodations at the Vatican are ready at the end of April.
Francis will begin his first Easter season mass as pope on Sunday when he celebrates Palm Sunday.
In the 10 days he has been the leader of the Roman Catholic Church, Pope Francis has made subtle changes in the lifestyle customary to his position. He has given up the papal ermine robe and red shoes for a white habit and black shoes, and abandoned his special limousine for the public bus. He also no longer greets guests from his elevated throne but at floor level.
On Thursday, the pope plans to celebrate the Mass of the Lord's Supper, which commemorates Jesus' Last Supper with his disciples, at a youth detention center, Casal del Marmo. He will wash the feet of young inmates.
"With this celebration at Casal del Marmo, Pope Francis will continue his custom, which is characterized by its humble context," the Vatican said in a statement.