The 'Vicar of Bahdad' said in his latest update that the situation in Iraq has "really deteriorated".
"The violence is so terrible and once again we are seeing so many of our own people fleeing to Turkey and Lebanon," he said.
Mr White said people in Baghdad "have nothing", as he told of a churchgoer who was found begging on the street by a member of the church staff.
"He asked her why she was doing this. She said all the food she had from church has run out and she has no money to pay her rent.
"We will give her everything she needs today but another example of the terrible needs. All may have left us but our Lord is still here."
Mr White said he had not seen so many people fleeing for several years.
"Iraq is no longer a news issue," he continued.
"We cannot blame the media for this. So many of the journalists have been targeted here and many killed, especially locals. The media have moved to the traumas elsewhere in the region."
He also expressed concern over the scores of people being killed in Syria, Israel and Gaza.
As fighting between Israel and Gaza entered a sixth day, health officials in Gaza said the conflict had killed 91 Palestinians so far. Israel has confirmed three deaths.
"The Middle East continues to be in turmoil," said Mr White.