"Capacities in the region are almost exhausted. But many thousands are still fleeing murder, violence and persecution. Among them are many people of the Christian faith," Interior Minister Wolfgang Schäuble said in an editorial in the Bild am Sonntag weekly.
He said that in meetings this week with interior ministers from Germany's states and with EU counterparts, "we will discuss how we as Germans and as Europeans can help in this worrying situation of Iraqi refugees, in particular those of the Christian faith, by taking them in."
"We have to help and offer them a home in European states until they can return to their homeland," Schäuble said. "I am seeing to it that Germany takes part in this."
Iraq's Christians, with the Chaldean rite the largest community, were said to total as many as 800,000 before the US-led invasion in 2003 but the number is now thought to be half that figure.
Widespread persecution including the bombing of churches and the murder of priests has forced hundreds of thousands to flee, mostly to neighbouring countries or to Kurdish northern Iraq.
Press reports in Germany have suggested that the country is prepared to accept as many as 30,000 Iraqi Christians.