Two of Mr Trump's Republican rivals, Marco Rubio and Jeb Bush, both Catholics, said they look to the Pope for spiritual guidance, not political direction.
Mr Rubio said the US has a right and an obligation to control its borders.
Mr Bush told reporters he "supports walls where it's appropriate" and that "Christianity is between he and his creator. I don't think we need to discuss that".
Jerry Falwell Jr, the president of conservative Christian Liberty University and a Trump supporter, told CNN that the Pope went too far,
"Jesus never intended to give instructions to political leaders on how to run a country," he said.