Story highlights Trump made the allegations Saturday without offering evidence

Graham hosted a packed town hall at Clemson University

(CNN) Sen. Lindsey Graham promised South Carolina residents Saturday that he would "get to the bottom" of President Donald Trump's unverified accusation earlier in the day that former President Barack Obama wiretapped the phones in Trump Tower.

"I'm very worried that our President is suggesting that the former President's done something illegally," the Republican lawmaker said at a packed town hall meeting. "I would be very worried if, in fact, the Obama administration was able to obtain a warrant lawfully about Trump campaign activity with foreign governments."

"So it's my job as a United States senator to get to the bottom of this," Graham added. "I promise you I will."

Trump made the claim Saturday, alleging without offering any evidence that his predecessor wiretapped the phones in Trump Tower, where his campaign was headquartered during the 2016 campaign.

"Terrible! Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found. This is McCarthyism!" Trump posted on Twitter.

Read More