Pope Francis made the comparison in his long speech, out of the head to members of the confederation of Italian family associations.
"Children must be accepted when they come, because God sends them, as God permits, even when they are sick," he said.
Pope Francis then talks about prenatal tests to determine whether the fetus has a disease or malformation.
"The first proposal, in this case, is 'Should we throw it away'? The killing of children. And to have a more peaceful life, innocent people are removed, "he said.
"I say it with pain. In the last century the whole world was underestimated by what the Nazis did to pursue racial purity. Today, we're doing the same thing, with white gloves, "he sneered.
Just for information, under the Nazi eugenics program, hundreds of thousands of people were forcibly sterilized and tens of thousands killed in an attempt to "cleanse" their descendants of physical or cognitive disabilities.
According to Wikipedia eugenika is a social philosophy which means improving the human race by removing diseased and disabled people and multiplying healthy individuals.