Republican nominee Trump had promised to stop Muslims coming to America if he is elected in November.
His proposal has since changed to ban only Muslims from country's which struggle with extremism.
Vice presidential nominee Mike Pence said that would mean a total ban on immigration from some Middle Eastern countries.
Inevitably that would also restrict access for Christians and Jews, he said.
Speaking to Charlie Sykes on US radio, Pence said: "The position that Donald Trump is advocating today is that we should temporarily suspend immigration from countries that have been compromised by terrorism, which I think is altogether fitting and appropriate."
When asked if that would mean a ban on Christians too, he said: "I think what you heard in the convention speech from Donald Trump, what we talked about out on the stump is that we would temporarily suspend from countries or from territories if you will, the caliphate obviously of ISIS [Islamic State] expands beyond one country, but to say that individuals that come from regions or countries that have been compromised by terrorism, we would suspend that immigration.
"I think that's appropriate until we develop a new vetting system."
Trump, who faces Hilary Clinton in the November poll, said in December 2015 he wanted a "total and complete shutdown of Muslims entering the United States".
Critics of Trump's proposal have called it "offensive and unconstitutional".
Meanwhile Trump's facing criticism amid claims he suggested gun owners could take matters into their own hands if Hillary Clinton becomes US president.
The Republican candidate made the remarks at a rally while talking about the Second Amendment - which gives Americans the right to bear arms.
One female senator said the comments made him a "pathetic coward who can't handle the fact that he's losing to a girl."
