"The Pope wanted this to be a sign of his closeness to all the faithful who suffer on account of their faith and the practising of their faith," said Father Lombardi.
"It's a gesture that should be seen as more than a simple meeting and instead become a symbol."
Pistelli said the family was in good health and would stay in Italy for a few days before departing for the United States to join the rest of the family.
Ibrahim's plight hit the headlines in May, when a Sudanese court sentenced the heavily pregnant doctor to death by hanging, prompting outrage around the world.
The judges found her guilty under Sharia law of apostasy - abandoning her Muslim faith - even though she was raised a Christian by her mother. Her father was Muslim but deserted the family.
The court also sentenced her to 100 lashes as it considered her marriage to Daniel Wani, a Christian from South Sudan who has US nationality, to be an act of adultery. The court was citing the extreme form of Sharia law that has been in force in Sudan since 1983.
Days after her conviction, Ibrahim gave birth to her second child in prison, after she refused to renounce her Christian faith during a four-day "grace period".
Following huge pressure from governments and campaigning groups, authorities in Khartoum overturned her conviction in June, but she was immediately rearrested while trying to flee Sudan using what prosecutors claimed were forged documents. She was later released.
- Independent