Trump's comments, which he made during an interview with ABC News, set off a political storm on Capitol Hill on Thursday, forcing Republicans to either break with Trump or remain silent amid a downpour of questions from reporters about accepting help from a foreign government.

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"Basically what I just told him is … you don't need to call the FBI cause somebody says they want to help your campaign, you need to call the FBI when somebody is trying to provide something of value to you that you think is inappropriate," Graham said.

Graham, who is up for reelection in a red state next year, was one of several Republicans who pushed back over Trump's claim that he would "look at" information about a political opponent even if it's offered by a foreign government. “I think you might want to listen. There’s nothing wrong with listening,” he told ABC. “It’s not an interference. They have information. I think I’d take it. If I thought there was something wrong, I’d go, maybe, to the FBI.” He added that "when it goes down the road of 'I've got dirt on your opponent,' that's a bright line. The answer is no."

“It would be totally inappropriate and it would strike at the heart of our democracy,” said Romney, an at-times vocal Trump critic who was the party's 2012 nominee for president.