Benedict's last public appearance was at a window of the castle, when he blessed the crowds below before retiring into seclusion.
The pope emeritus is expected to move back to Vatican City at the end of April, once restoration work on a small monastery within its grounds is complete. There, he will devote himself to prayer and study.
Benedict "has attentively followed the events of recent days," including Francis' inauguration Mass before crowds of well wishers and dignitaries, the Vatican said.
When the last pope to resign, Gregory XII, stepped down in 1415 it was to help resolve the worst institutional crisis in the church's history -- a schism that had led to three rival claimants to the papacy.
And when former hermit Pope Celestine V resigned in 1294 after less than six months in office, he was imprisoned soon afterward by his successor, Pope Boniface VIII.
Busy week ahead
Pope Francis, meanwhile, is starting to get to grips with his new role now that the pomp and ceremony of his inauguration is out of the way.
On Friday, he met with the Vatican diplomatic corps and thanked them for the work they do to "build peace and construct bridges of friendship and fraternity" with some 180 states around the world.
"Through you I encounter your peoples, and thus in a sense I can reach out to every one of your fellow citizens, with their joys, their troubles, their expectations, their desires," he said.
The coming week, which leads up to Easter Sunday, will be a busy one for the new pontiff, starting with Palm Sunday Mass.
On Thursday, Francis will break with tradition by celebrating the Mass of the Lord's Supper -- which is centered on the gesture of the washing of feet -- at the Casal del Marmo youth detention center, the Vatican said.
The service has in past years been held at the grand Basilica of St. John Lateran, the official seat of the bishop of Rome.
"In his ministry as Archbishop of Buenos Aires, Cardinal Bergoglio used to celebrate the Mass in a prison or hospital or hospice for the poor and marginalized," the Vatican said in a statement.
"With this celebration at Casal del Marmo, Pope Francis will continue his custom, which is characterized by its humble context."
It will not be the first time Francis visits the prison. He was there in March 2007 to celebrate Mass.