No date had ever been set, but the local church expected the pope to visit next month and a Vatican advance team recently traveled to Baghdad.
Iraq reportedly told the Vatican that it could not organize the trip because of the U.N. embargo and the no-fly zone. The brief Vatican statement did not elaborate.
John Paul had hoped to visit Ur, believed to be the birthplace of Abraham, as part of a millennium tour of pilgrimage sites in the Middle East.
The U.S. and British governments and the Iraqi political opposition in exile have expressed misgivings about such a visit, saying it would only be used by President Saddam Hussein for propaganda purposes.
John Paul said the visit would be purely religious in nature and have no political significance.
Since the 1991 Persian Gulf War, allied warplanes have been patrolling so-called no-fly zones in northern and southern Iraq. The country is under U.N. sanctions for having invaded Kuwait.
The Vatican statement said Iraqi authorities had informed the Vatican secretary of state that "abnormal conditions" resulting from the embargo and no-fly zone prevent Baghdad from adequately organizing a stop in Ur.
The Iraqi government never issued a formal invitation.
A church leader in Baghdad said the trip has only been delayed, not canceled, and claimed the visit was put off because the pope's security could not be guaranteed.
"Americans and English have the entire airspace in their hands," the Chaldean church patriarch Rafael Bedaweed told the Vatican's missionary news service, Fides. He said if anything happened to the pope during the visit, "certainly the international community would blame Iraq."
It is not the first time that a papal trip was put off despite visits by Vatican advance teams. Trips to Beirut and Sarajevo were delayed out of security concerns but the pope later visited both cities.
John Paul has also expressed a desire to visit Russia and China, but neither country has invited him.
The pope is expected to visit the Holy Land in March, but tensions over the building of a mosque near a church have raised questions about the itinerary.
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