Asked by reporters Tuesday in Elko, Nevada, if Bush believes that Trump is a Christian, the former Florida governor expressed some doubt.
"I don't know what he is. I just don't think he has the kind of relationship that he says he has if he can't explain it in any way that shows he's serious about it," Bush said.
"Accepting the fact that we make mistakes and seek forgiveness, that's one of the tenants of Christianity that everybody can agree on," he added. "We're all sinners. Some more than others."
Falwell, president of Liberty University -- the world's largest evangelical university -- said in a statement he's supporting the GOP front-runner because he is a "successful executive and entrepreneur, a wonderful father and a man who I believe can lead our country to greatness again."
The endorsement came in spite of some flubs on Trump's part that drew attention to his faith. When speaking at Liberty last week, Trump muffed his delivery of a Bible passage, citing "two Corinthians," rather than "Second Corinthians," as it is commonly known.
Earlier this year, he told a crowd of evangelicals in Iowa that he believes in God but when asked if he has ever asked God for forgiveness for his actions, Trump said, "I am not sure I have."
"I just go on and try to do a better job from there. I don't think so," he said. "I think if I do something wrong, I think, I just try and make it right. I don't bring God into that picture. I don't."
For his part, Bush converted to his wife's faith of Catholicism in the mid 1990s and regularly invokes his faith in his stump speech. He also spoke at Liberty last summer.
"For a guy who's stated he's never sought forgiveness, it's hard to imagine how someone who is a strong believer (like Falwell) would embrace that idea," Bush said. "There may be other reasons why President Falwell is supporting him, I respect that but Trump views all this not from a position of his faith, he views it all as politics. I think faith goes way beyond politics."
Earlier Tuesday, Bush's Twitter account linked to a statement from the anti-abortion rights group Susan B. Anthony List
saying Trump is "unacceptable," and urging voters to back anyone but the real estate titan.
Bush has previously attacked Trump for flip-flopping on abortion.
"He's playing this for political purposes for sure. I'd rather have him actually at least accept the fact that we're all imperfect under God's watchful eye and that we should seek forgiveness and that ultimately to be a believer is accepting Christ as your savior," Bush told reporters on Tuesday. "It's not that where you're born doesn't define your Christianity or being an evangelical, it's your relationship with the Lord and if he can get to that I'd feel more comfortable with it."
Bush's comments came after his campaign held a rally before about 135 people in the small town of Elko in northeastern Nevada. He flies Tuesday night to Des Moines, Iowa, where he'll attend the GOP debate Thursday and then embark on an aggressive three-day campaign schedule across the state before the caucuses on Monday.