The pontiff suggested late Wednesday night that the GOP front-runner's plans to deport undocumented immigrants and build a wall between the U.S. and Mexico signify that he "is not Christian."
Francis, returning to Rome after a six-day visit to Mexico that included a stop to say mass at the U.S.-Mexico border, told a reporter who asked him about Trump aboard the papal airliner: "A person who thinks only about building walls, wherever they may be, and not building bridges, is not Christian. This is not in the gospel."
Francis stopped short of saying American Catholics should not vote for Trump, however.
"I am not going to get involved in that," he said. "I say only that this man is not Christian if he has said things like that."
Trump wasted no time retaliating in a statement:
"For a religious leader to question a person's faith is disgraceful. I am proud to be a Christian and as President I will not allow Christianity to be consistently attacked and weakened, unlike what is happening now, with our current President."
"No leader, especially a religious leader, should have the right to question another man's religion or faith," he said, adding that Mexico's government has "made many disparaging remarks about me to the Pope."
"If and when the Vatican is attacked by ISIS, which as everyone knows is ISIS's ultimate trophy, I can promise you that the Pope would have only wished and prayed that Donald Trump would have been president."
Siding with Francis on this one is Christopher Hale, executive director of Catholics in Alliance for the Common Good, who tells PEOPLE: "Pope Francis is absolutely right: There's nothing Christian about building walls. Donald Trump's immigration stance is a total affront to the gospel of Jesus Christ."
"During this election year, the American people can take Pope Francis' advice and build bridges, or heed the advice of Donald Trump and build walls. If Francis is right, all walls eventually crumble."