Trump said among "other things" that he read about wiretapping was a New York Times article and a Fox News report.
"I said, 'Wait a minute, there's a lot of wiretapping being talked about,'" Trump said. "I've been seeing a lot of things."
But the examples he put forward don't appear to back up his claim that Obama ordered a wiretap of Trump Tower in New York.
The New York Times article that Trump is mentioned never claimed Obama ordered a wiretap of Trump Tower, and Fox News never independently reported the story.
Trump said that while he didn't want to discuss it, the White House "will be submitting things before the [House Intelligence] Committee very soon that hasn't been submitted as of yet."
Rep. Devin Nunes, the chairman of the House Intelligence Committee, said earlier on Wednesday that he didn't think "there was an actual tap of Trump Tower."
Trump raised the possibility that he would speak about his claim in the next week, perhaps before the committee goes public with any findings.
"I mean, let's see whether or not I prove it," Trump said. "But I think we have some very good stuff. And we're in the process of putting it together, and I think it's going to be very demonstrative."
Asked why he didn't just approach the intelligence agencies to verify whether his claim is true, Trump said he didn't "want to do anything that's going to violate any strength of an agency."
"And don't forget, when I say 'wiretapping,' those words were in quotes," Trump said. "That really covers, because wiretapping is pretty old fashioned stuff, but that really covers surveillance and many other things. And nobody ever talks about the fact that it was in quotes, but that's a very important thing."
But only two of his four tweets related to wiretapping included the term in quotes.