Donald Trump has backtracked on some harsh criticism of Pope Francis for saying anyone pledging to build a wall along the Mexican border with the United States cannot claim to be a Christian.

The Pope ignited a fierce response from U.S. Republican Party presidential candidate hopeful Trump when, without naming him, he questioned his Christian credentials. His comments immediately became part of the U.S. presidential debate.

"Anyone, whoever he is, who only wants to build walls and not bridges is not a Christian," Francis said on the papal flight from Mexico in answer to a question from a journalist.

"Vote, don't vote, I won't meddle. But I simply say, if he says these things, this man is not a Christian," Francis said.

"We need to see if he really said them and for this I will give him the benefit of the doubt."

On a campaign rally stop in South Carolina, which holds its Republican primary this weekend, Trump hit back saying, "For a religious leader to question a person's faith is disgraceful.

"I'm 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," said Trump, who is a Presbyterian.

Trump has littered his campaign with comments seen as derisive of women, Mexican immigrants and Muslims, most of whom are recent immigrants to the United States.

During his speech Trump declared that "Mexico is the new China" and he used the Pope's concluded visit as an example.

"The Pope was in Mexico. Do you know that? Does everyone know that?

"He said negative things about me because the Mexican government convinced him that Trump is not a good guy because I want to have a strong border, I want to stop illegal immigration, I want to stop people from being killed."

Trump added, "The Mexican government fed the Pope a tremendous amount of stuff about 'Trump is not a good person'.... Can you imagine that?"

He argued that Mexican officials, were "using the Pope as a pawn," noting, "The Pope only heard one side of the story."

Later the same day at a televised town hall meeting in Greenville, South Carolina, Trump toned down his comments on the pontiff.

"I have a lot of respect for the Pope. He has a lot of personality and I think he's doing a very good job, he has a lot of energy."

Trump said the Francis was misinformed when he criticized the proposed wall, because he was unaware of the drugs coming in and the other security problems.

After the Pope's comments on Trump's immigration policy, Vice President Joe Biden said the feud is "not a hard call," NBC News online reported.

"Pope Francis, Donald Trump? That's not a hard call for me, not even close," Biden said. "I am not a theologian nor am I priest or a minister, but I think that building walls is fundamentally contrary to what made this country what it is."