GOP rival: Donald Trump is getting his support from the 25% of my party that thinks Obama is Muslim

Presidential candidate Sen. Lindsey Graham (R-South Carolina) unloaded Tuesday on real-estate mogul Donald Trump, using some of his harshest rhetoric yet.

Graham argued Tuesday on CNN that his Republican rival is appealing to the same people who believe in conspiracy theories about President Barack Obama's birthplace or religion.

"Twenty-five percent of our party probably thinks that Obama was born in Kenya - or at least wants to believe that. There are 25% of our party [that] wants him to be a Muslim because they hate him so much," Graham said.

"So there's a dark side of politics that Mr. Trump's appealing to," he added.

Graham cited Trump's controversial comments about illegal immigration and Fox News host Megyn Kelly. Trump frequently accuses the Mexican government of intentionally sending "rapists" across the border and he has shared multiple tweets calling Kelly a "bimbo," among other things. (Graham didn't mention it, but Trump was also once one of the most high-profile people questioning Obama's birthplace.) 

"The policies that Mr. Trump is proposing are demagoguery. His approach to describing illegal immigrants are hurting us with Hispanics. The way that he attacks women is going to be a death blow to the future of our party," Graham said during the CNN interview. 

Graham, who has prominently feuded with Trump in the past, continued to unleash a scathing criticism. 

"He is shallow. He is ill-prepared to be commander-in-chief. He doesn't know what he's talking about in terms of how our laws work. He says the worst things possible about immigrants and women. And he's a complete idiot when it comes to Mideast policy," he said. "His policy prescriptions are complete gibberish."

Trump, who polls show is the Republican front-runner, has declared that Graham is little more than an annoyance. While campaigning in Graham's home state last month, Trump publicly revealed the senator's personal cell-phone number. And Trump frequently mocks Graham's low standing in the polls.

Indeed, Trump had a particularly sarcastic tweet directed at Graham on Tuesday:

For his part, Graham said if the two faced off in South Carolina, he would "beat his brains out."

"Come to South Carolina and I'll beat his brains out," Graham said of Trump. "I know my state. This is a silly season in politics."

View Graham's CNN interview below: