Cardinal Angelo Scola of Milan and Cardinal Bechara Rai, the patriarch of the Maronite Catholic Church, visited homeless families living in tents or makeshift shelters, and the nuns, priests and other Christians ministering among them, last Friday.
The cardinals also blessed children, toured a medical clinic and prayed at a shrine to Mary, the mother of Jesus.
Kurdistan's Interior Minister Karim Sinjari, along with the Chaldean Patriarch of Baghdad Louis Sako and the Chaldean Bishop of Irbil Bashar Warda, greeted the two cardinals as they arrived at Irbil airport for the one day visit.
Cardinal Rai said in a statement: "Our main demand is that they [the Christians] return to their homes and lands in dignity.
"We have trusted the international coalition in that.
"But, unfortunately, the terrorist groups are still growing and advancing."
During the one-day trip, he also said: "Here we should ask: Where are they [Islamic State] receiving this strength from?
"Why is ISIS being treated as a state and not a terrorist group?
"We don't speak the language of killing, but that of rights.
"The international community should not remain silent toward the violation of the rights of a whole people.
"Christians should remain in Iraq because their history is rooted in Iraq, where they have lived alongside Muslims and built common civilisations.
"Their future is here, too, and they cannot let go of this land."
