A spokeswoman for the United Nations High Commissioner for Refugees says some 1,000 families have left Baghdad and Mosul province since an .
Melissa Fleming says the flight of Christians to other parts of Iraq and abroad has become "a slow but steady exodus."
UNHCR also said Friday it is "dismayed" European governments are deporting failed Iraqi asylum seekers to areas of the country it doesn't consider safe.
Fleming cited a Dec. 15 deportation flight from Sweden that included at least five Christians from Baghdad.
"Those who fled the latest violence - many in a panicked rush, with only the possessions they could pack in cars - warned the new violence presages the demise of the faith in Iraq," the Sydney Morning Herald reported Friday, adding that "several evoked the mass departure of Iraq's Jews after the founding of the state of Israel in 1948."
"It's exactly what happened to the Jews," said Nassir Sharhoom, 47, who fled last month to the Kurdish capital, Erbil, with his family from Dora, a once-mixed neighborhood in Baghdad. "They want us all to go."
On Thursday, , denouncing lack of freedom of worship as an "intolerable" threat to world security.
The message reflected a pressing concern by Benedict in recent months for the plight of Christian minorities in parts of the world, especially in the Middle East.
"Sadly, the year now ending has again been marked by persecution, discrimination, terrible acts of violence and religious intolerance," Benedict lamented in the message for World Peace Day, celebrated by the church on Jan. 1, but traditionally released in advance
He wrote that he was especially thinking of Iraq ",which continues to be a theater of violence and strife" as it aims for stability and reconciliation.
Benedict singled out the "reprehensible attack" on a Baghdad cathedral during Mass in October, killing two priests and more than 50 other worshippers, as well as attacks on private homes that "spread fear within the Christian community and (create) a desire on the part of many to emigrate in search of a better life."
The Vatican voiced concerns that the steadily flight of Christians from Iraq will effectively eliminate the ancient community there.
"At present, Christians are the religious group which suffers most from persecution on account of its faith," the pontiff asserted, and cited Christian communities suffering from violence and intolerance particularly in Asia, Africa, the Middle East and the Holy Land.
"This situation is intolerable, since it represents an insult to God and to human dignity" as well as "a threat to security and peace," Benedict wrote in one of the 17-page-long message's strongest passages.
He appealed to authorities to "act promptly to end every injustice" against Christians.