The Pope was speaking to migrants at the Basilica of St. Bartholomew on Saturday about a man he met at a refugee camp on the Greek island of Lesbos last year.
"I don't know if he was able to get out of that concentration camp, because the refugee camps -- many -- are concentration (camps), because they are so crowded with people," the Pope said in Italian.
The AJC issued a statement asking the pontiff to reconsider his "regrettable" choice of words.
"The conditions in which migrants are currently living in some European countries may well be difficult, and deserve still greater international attention, but concentration camps they certainly are not," said AJC CEO David Harris.
"The Nazis and their allies erected and used concentration camps for slave labor and the extermination of millions of people during World War II," he said.
"There is no comparison to the magnitude of that tragedy."
The Vatican's web site said Francis was speaking off the cuff when he said the refugee camps are like "concentration camps, while international agreements seem to be more important than human rights."