All the groups, generously funded by American churchgoers, are likely to do a magnificent job in offering water, food, medical help and comfort to a traumatised population. But they are causing alarm among Muslims, who fear vulnerable Iraqis will be cajoled into conversion, and Christians, some of whom warn that the missionaries will be prime targets in an unpacified Iraq.
Muslim worries have been heightened because the man leading the charge into Iraq is the Rev Franklin Graham, who delivered the invocation at President Bush's inauguration, the son of Billy Graham and a fierce critic of Islam. He is on record as calling it a "wicked, violent" religion, with a God different from that of Christianity. "The two are different as lightness and darkness," he wrote.
He runs an organisation called Samaritan's Purse, whose workers are in Jordan, waiting to move into Iraq. It has a strong record of charitable help built up over more than 30 years, but its official aim is clear: "The organisation serves the church worldwide to promote the gospel of the Lord Jesus Christ."
Of late, Mr Graham has avoided inflammatory statements and declined to speak to the Guardian. He did, however, write an article for the Los Angeles Times yesterday designed to mollify his critics, insisting that Samaritan's Purse will offer help to Iraqis without religious strings attached. "Sometimes the best preaching we can do is simply being there with a cup of cold water, exhibiting Christ's spirit of serving others," he said.
Ibrahim Hooper, of the Washington-based Council on American-Islamic Relations was unimpressed, saying the groups involved were "despicable and deceitful". Of Mr Graham, he said: "This guy has repeatedly stated that Islam is intentionally cruel. I fail to see how such a person can be a positive influence in a Muslim country. Humanitarian relief is just a cover. Their basic motivation is conversion. These groups train workers to go in under the guise of relief to convert people away from their faith.
"I know this because I've been on their training courses. There's a technique known as contextualisation. You never say directly you're Christian. You take chairs out of the church to make it look like a mosque. You grow a beard. You dress your wife in Islamic attire. They know they're not welcome."
Also moving into Iraq are the Southern Baptists, the second largest religious group in the US after the Catholics and the most powerful component of the Christian conservative movement. They are perhaps the strongest pro-Bush, pro-Iraq war and pro-Israel political force in the US.
Their coordinator in Oklahoma, Sam Porter, insists that humanitarian aid is the prime objective of the Iraqi relief operation; the church has 25,000 trained volunteers who help in disaster relief in the US and elsewhere.
But he added: "If someone says 'Why would you to come to Iraq to serve in an impoverished, war-stricken country?' we would say it was because of the love that the Lord Jesus Christ put in our hearts. If a country opens up for evangelical missions to go there, we go. We believe strongly that Jesus Christ is the son of God and we intend to proclaim that."
Some Christian commentators are alarmed that missionaries blundering into an unstable country of which they know little would be in danger. Three Baptist missionaries were shot and killed in Yemen last December by a Muslim extremist, who said he did it because "they were preaching Christianity in a Muslim country".
One evangelical writer, Richard Mouw, of beliefnet.org, warned the groups: "We must do this with a genuine desire to serve human needs. If this is viewed as a pretence for evangelism it will only hurt the Christian cause, and perhaps further endanger the lives of the 600,000 Christians in Iraq."
Jonathan Bonk, editor of the International Bulletin of Missionary Research, says that many strong evangelicals cannot separate their charitable work from spreading their faith. "It's not a crafty attempt to proselytise. It's an earnest attempt to share what they hold most dear. That's true of all the proselytising religions, including Islam.
"The difficulty in Iraq won't be because the evangelists are Christian, but because they're western. If they aggressively evangelise, that's a problem. But they're going to be in danger whether they say anything or not. As symbols of the west, and what the west represents, they are targets."