The pope's comments appearing to question the authenticity of Donald Trump's own Christian faith have some conservatives running to the candidate's defense.

The fracas began over the issue of immigration with Pope Francis criticizing Trump's plan to build a wall at the border to keep illegal Mexican immigrants out. Francis said this wasn't Christian. Trump begged to differ, calling it "disgraceful" that the pontiff would question his faith.

Thursday's back-and-forth has drawn comments from some Christian conservatives who think the pope should have stayed out of the political fray.

"Being a Catholic myself - and I've earned that identity going to Catholic high school and college - my whole training is learning in Catholicism - I am very disappointed in the pope coming out against Donald Trump," said actor Jon Voight in a text to Fox News Thursday.

"Men or the cloth should not get involved in political campaigns," he added.

"If he's concerned about all our illegal aliens, let the Vatican take in a few million. They're as rich as any city in the world, and then His Holiness can take care of them."

Longtime conservative strategist Richard Viguerie called it a "grave disappointment" that the pope decided to pick a fight with Trump over the border wall, rather than use this influence to condemn other U.S. policies, like legal abortion and same-sex marraige.

"The Pope’s remarks about illegal immigration and his subsequent choice to pick a fight with a secular politician over a matter of secular government policy, while ignoring the assaults on Christian moral precepts that are now shaking the very foundations of our culture were a grave disappointment to hard-pressed Catholics and other Christians who are fighting to defend the traditional moral underpinnings of Western civilization." 

The pope, responding earlier in the day to a question aboard the papal plane about Trump’s promise to build a U.S.-Mexico border wall, had said: "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."

Trump quickly responded: “For a religious leader to question a person’s faith is disgraceful,” he said.

Pope Francis weighed in just hours after he prayed at the Mexico-U.S. border for migrants who died trying to reach the United States. The pope did not definitively say Trump is not a Christian. Not having heard Trump's border plans independently, Francis said he'd "give him the benefit of the doubt."

But he said: "I'd just say that this man is not Christian if he said it this way."

The comments escalated what had been an otherwise cordial dispute between the two in recent days over immigration policy.

Trump said in response he is a “proud” Christian and accused the Mexican government of using the pontiff for its own purposes.

“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 United States. He doesn’t see how Mexican leadership is outsmarting President Obama and our leadership in every aspect of negotiation,” he said. “…They are using the pope as a pawn and they should be ashamed of themselves for doing so, especially when so many lives are involved and when illegal immigration is so rampant.”

Trump also said that “if and when the Vatican is attacked by ISIS … I can promise you that the pope would have only wished and prayed that Donald Trump would have been president because this would not have happened.”

A Vatican spokesman said Friday that the pope was speaking to his own "general attitude," adding, "the pope said something we know well, when we follow his teachings and positions, that we don't have to build walls but bridges."

Trump has had heated and high-profile feuds with several of his GOP rivals on the primary campaign trail, including Ted Cruz, Jeb Bush and former candidate Rand Paul.

But the fight with the Vatican is something entirely different.

It started on a more subdued note. Last week, Trump told Fox Business Network that he did not believe Pope Francis understood what he called "the danger of the open border we have with Mexico."

Trump has repeatedly vowed to build a wall along the entire border with Mexico – and make Mexico pay for it. All along, he's made combating illegal immigration a centerpiece of his presidential campaign, claiming credit for kickstarting the debate which now features heavily in the GOP primary race.

The Associated Press contributed to this report.