Pope Francis assailed Republican presidential candidate Donald Trump's views on US immigration as "not Christian" on Thursday, prompting the billionaire businessman to reprimand the religious leader as "disgraceful" for questioning his faith.

No stranger to controversy, Trump, the longtime party front-runner in national opinion polls, has vowed if elected president to build a wall between the US and Mexico to keep out immigrants who enter illegally.

In a freewheeling conversation on his flight home from a visit to Mexico, Francis told reporters, "A person who thinks only about building walls, wherever they may be, and not building bridges, is not Christian."

Trump, a real estate developer and former reality TV star, said, "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," Trump said in a speech in Kiawah Island, South Carolina.

"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," Trump said.

"No leader, especially a religious leader, should have the right to question another man's religion or faith," Trump said.

Trump has said he would deport millions of illegal immigrants if he wins his party's nomination and then the November 8 election. Last week, responding to the pope's plan to visit the US-Mexican border, he said that Pope Francis did not understand the Mexican border issues.

"The pope is a very political person. I think he doesn't understand the problems our country has. I don't think he understands the danger of the open border that we have with Mexico," Trump told the Fox Business Network.

Asked about being called a "political person", Francis said on Thursday, "Thank God he said I was a politician because Aristotle defined the human person as 'animal politicus.' So at least I am a human person."

The pope said, however, he did not want to advise American Catholics on whether or not to vote for Trump.

Social media erupts

The pope's remarks and Trump's response lit up social media with many Twitter users speculating on how Trump would move on from the pope's withering comment. Author Dan Dicker @Dan_Dicker tweeted, "Let's see @realDonaldTrump insult his way out of this."

Trump's social media director Dan Scavino @DanScavino tweeted, "Amazing comments from the Pope - considering Vatican City is 100% surrounded by massive walls."

In a written statement Trump accused the Mexican government of making disparaging remarks about him to the pope "because they want to continue to rip off the US, both on trade and at the border, and they understand I am totally wise to them.

"The pope only heard one side of the story - he didn't see the crime, the drug trafficking and the negative economic impact the current policies have on the US. He doesn't see how Mexican leadership is outsmarting President Obama and our leadership in every aspect of negotiation."