The refugees were among those driven from their homes around Mosul last summer in an offensive by the jihadist Islamic State group (IS), and the pontiff used a satellite phone connection provided by Catholic channel TV 2000 to offer them his support.
"Dear brothers, I am close to you, very close to you in my heart," the pope was quoted as telling the refugees by Italian press agency AGI.
Many Christians have fled fighting to seek refuge in Arbil.
"The children and the elderly are in my heart," Francis also told the Iraqi refugees in the Ankawa camp, just hours before celebrating midnight mass in Saint Peter's basilica.
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"Innocent children, children who have died, exploited children.... I am thinking, too, about grandparents, about the older people who have lived their lives, and who must now bear this cross."
This Christmas has been particularly difficult for the estimated 150,000 Christians displaced in Iraq, the Chaldean Patriarch Louis Sako told AFP in Baghdad.
"Particularly during this Christmas period, they needs reassuring signs. They must be told that they have not been abandoned or forgotten," he said.
On Monday, the pope addressed a long letter of support to Christians in the region, urging them to "persevere" despite the difficulties they face.
In it, he denounced IS as a "terrorist organisation of a size that was unimaginable before, committing all types of abuses... (and) striking some among you who have been brutally chased from your lands, where Christians have been present since apostolic times."
Francis lamented the suffering of women, children and the elderly who "must face the harshness of winter without a roof," and called for concrete support from the wealthier churches.