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Rep. Jason Chaffetz, R-Utah, said he has yet to see any evidence that former President Barack Obama ordered illegal wiretapping of Trump Tower during the election, as Donald Trump alleged on Twitter this weekend — but the Republican congressman didn't deny that such proof could exist.

"I learned a long time ago, I'm going to keep my eyes wide open," Chaffetz said on a "CBS This Morning" segment that aired Monday. "You never know when you turn a corner what you may or may not see, but thus far I have not seen anything directly that would support what the president has said."

Trump tweeted four times early Saturday morning accusing Obama of tapping his skyscraper campaign headquarters "during the very sacred election process." The president continued to say "this is Nixon/Watergate."

"Terrible! Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found," he said in one of the messages posted on social media. "This is McCarthyism!"

Trump offered no evidence to support the allegations. And in response to a question Monday during an off-camera press gaggle, White House Press Secretary Sean Spicer said the president would like Congress to look into the issue.

"Neither the White House nor the president will comment further until such oversight is continued," Spicer said.

FBI Director James Comey has disavowed the assertion and asked the Justice Department to refute it. Obama has also said there is no truth behind Trump's statements.

Also, James Clapper, former director of national intelligence, told CNN that the intelligence agencies he oversaw did not wiretap Trump last year, nor did the FBI obtain a court order to do so.

Chaffetz, chairman of the House Oversight and Government Reform Committee, seemed open to a congressional investigation of the wiretap allegations, noting that if the president's tweets are accurate, "the paper trail should be there" to prove it.

"I got to believe, I think [Trump] might have something there, but if not, we're going to find out," Chaffetz said in the interview, later adding: "It's going to take us some time to unravel this."

An inquiry, he said, would be led by the House Intelligence Committee, which Rep. Chris Stewart sits on. Stewart, R-Utah, declined to comment on whether Trump's assertions had merit, but said there will be an investigation of the allegations.

"There's been an accusation made," he said, "and we need to find out if that accusation is true or not."

He told the Deseret News that the allegation "didn't come completely from left field" and were "not made out of thin air."

Twitter: @CourtneyLTanner