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She arrived in Italy to jubilant scenes following intense international efforts to free her, AP said.
Ms Ibrahim and her husband, Daniel Wani, personally thanked the pontiff for his support.
The Pope, in turn, thanked her for her courage and staying true to her Christian faith throughout her almost year-long ordeal.
Father Federico Lombardi, the Vatican spokesman, described the half-hour meeting as "calm and affectionate" and said that the Pope wanted it to be a "gesture of support to all those who suffer for their faith, and living in difficult or restrictive situations".