– President Donald Trump said Wednesday that he thought that former national security adviser Susan Rice may have committed a crime by seeking the identities of Trump associates who were swept up in the surveillance of foreign officials by U.S. spy agencies and that other Obama administration officials may also have been involved.

The president provided no evidence to back his claim. Current and former intelligence officials from both Republican and Democratic administrations have said that nothing they have seen leads them to believe that Rice's actions were unusual or unlawful.

When Americans are swept up in surveillance of foreign officials by intelligence agencies, their identities are supposed to be obscured, but they can be revealed for national security reasons, and intelligence officials say it is a regular occurrence.

"I think it's going to be the biggest story," Trump said in an interview in the Oval Office. "It's such an important story for our country and the world. It is one of the big stories of our time."

He declined to say whether he had personally reviewed new intelligence to bolster his claim but pledged to explain himself "at the right time."

When asked whether Rice, who has denied leaking the names of Trump associates under surveillance by U.S. intelligence agencies, had committed a crime, the president said, "Do I think? Yes, I think."

Rice has denied any impropriety. In an interview Tuesday with MSNBC, she said: "The allegation is that somehow the Obama administration officials utilized intelligence for political purposes. That's absolutely false."

Trump, who has a history of promising to produce evidence to back up his unverified claims, and failing to do so, did not make it clear what crime he was accusing Rice of committing. It is legal and not unusual for a national security adviser to request the identities of Americans who are mentioned in intelligence reports provided.

Intelligence officials said any requests that Rice may have made would have been handled by the intelligence agency responsible for the report, which in most cases would have been the National Security Agency.

Leaking classified information could be a crime, but no evidence has surfaced publicly indicating that Rice did that and she flatly denied doing so in her interview with MSNBC. "I leaked nothing to nobody, and never have and never would," Rice said.

Trump criticized media outlets for failing to adequately cover the Rice controversy and singled out Fox News host Bill O'Reilly for praise, despite a Times report of several women who have accused O'Reilly of harassment. The president then went on to defend O'Reilly, who has hosted him frequently over the years.

"I think he's a person I know well — he is a good person," said Trump, who during the interview was surrounded at his desk by a half-dozen of his highest-ranking aides, including economic adviser Gary Cohn and chief of staff Reince Priebus, along with Vice President Mike Pence.

"I think he shouldn't have settled; personally I think he shouldn't have settled," said Trump. "Because you should have taken it all the way. I don't think Bill did anything wrong."