Some of the visitors are the Pope's closest aides: Cardinal Angelo Sodano, Vatican secretary of state; Cardinal Camillo Ruini, the Pope's vicar for Rome; Archbishop Leonardo Sandri, substitute of the Vatican Secretariat of State.
Other visitors are from other faiths. The chief rabbi of Rome, Riccardo Di Segni, visited today accompanied by five people.
"We are a delegation of the Jewish community of Rome who have come to ask for direct news on the Pope's health at this further moment of trial," said the rabbi.
"We express our solidarity to him with the hope that he will be able to leave with good health. We have recited a psalm, as we usually do when we attend to a suffering patient," he added before leaving the hospital.
After the operation on Thursday night, Gianni Letta, Cabinet undersecretary and a close adviser of Italian Prime Minister Silvio Berlusconi, spoke with the Pope's doctors.
Waiting in the hospital's reception hall was Sister Rosetta Donato, of the Daughters of Mount Calvary, who visits the Gemelli every time the Pope is admitted, because "I spoke with him in Castel Gandolfo in 1985 and offered him my life."
The nun added that she prays at the hospital because her congregation's charism is "to be close to every human calvary. And this is the Pope's calvary." She said she also shares the suffering of the children and elderly in the hospital.
"For me the Pope is very special, I feel the pain characteristic of children, and I realize that the Pope has taught me to respect the dignity of the person," she added.
Francesca Immacolata Sciaughi, from Calabria in southern Italy, came with a floral arrangement and a written message to the Pope from the law students of La Sapienza University in Rome.
She said that the law students, who will finish their classes Monday, are offering their studies for the Pope "because we want the Holy Father to continue to be our guide. We need him and he has made us understand that we must put our knowledge at the service of others."
The law student added: "For me, he is like a father, as I don't have a father. He is a person who inspires my life, in each of the smallest things. He must continue to journey with us."
Beginning tonight, at the initiative of the Pastoral Center of Sacred Heart University, the students of the Gemelli faculty of medicine and surgery, with the help of spiritual assistants, will hold a prayer vigil for the Holy Father in each of the six student residences.
On Saturday, Monsignor Gianni Ambrosio, general ecclesiastical assistant of Sacred Heart University, will lead a prayer service for the Pope in the third-floor chapel of the Gemelli Polyclinic, which will be attended by students, professors and hospital personnel.