Francis held a "cordial" meeting with the leader at the Vatican on Wednesday morning.
The Vatican's Foreign Secretary, British Archbishop Paul Gallagher, was also in attendance.
Church officials said the pontiff spoke about the "good state of bilateral relations between Iraq and the Holy See" and the life of the Church in the country.
However it added that Francis raised the situation of Christians and ethnic and religious minorities living in Iraq.
He is said to have spoken about the importance of their presence and the need to protect their rights.
A statement added that the pair agreed the need for interreligious dialogue.
Christians are persecuted by Islamic State in large parts of Iraq but even in areas still under control of government forces, believers face threats and violence.
