"Many left with little money and need help," Redmond told reporters in Geneva, where the agency is headquartered.
He said a Christian nurse told his agency the threats started months ago with phone calls, letters, and messages left on doors.
Another woman said she fled when she heard of a Christian who was murdered. "We were the hard core that never wanted to leave Iraq, even with the tense environment," the woman, who fled to Syria, was quoted by the agency as saying.
The agency has delivered relief supplies to more than 1,700 Christian families now displaced in the north of the country, Redmond said. Most are living in churches, monasteries, and the homes of relatives in nearby Christian villages and towns.
No group has claimed responsibility, but Sunni extremists are believed to be behind the campaign, which is taking place despite US-Iraqi operations aimed at rousting insurgents.
In Baghdad, meanwhile, a hard-line Shi'ite cleric and lawmaker called for rational debate on a draft US-Iraqi security pact that would give the United States a legal basis for keeping its forces in Iraq for three more years.
Jalaluddin al-Saghir told worshipers that the government was still tinkering with the deal, which would also grant Iraq limited authority to try US soldiers and contractors charged with serious crimes. "The politicians should think about Iraq's interests. They should not seek to break the unity of Iraqi society," he said.
Saghir is a senior figure in the Supreme Islamic Iraqi Council, which dominates the government with Prime Minister Nouri al-Maliki's party. The council has called for changes to the deal.
There was however a different message in mosques frequented by supporters of anti-US Shi'ite leader Moqtada al-Sadr.
Sheik Abdul-Hadi al-Mohammadawi, an aide to Sadr, praised the tens of thousands who marched through Baghdad last week calling for an end to the US presence in Iraq.
READER COMMENTS »
View reader comments » Comment on this story »