Speaking to The New York Times
Wednesday, Trump said, "I think it's going to be the biggest story."
He continued,"It's such an important story for our country and the world. It is one of the big stories of our time."
Trump, asked by the Times, if he believed Rice committed a crime, responded, "Do I think? Yes, I think."
Trump offered no evidence to back his allegations or any names of other Obama administration officials he said were also involved. He did not suggest that his assertions came from new intelligence reports but said he would explain himself further "at the right time."
In response, Erin Pelton, a spokesperson for Rice, told CNN: "I'm not going to dignify the President's ludicrous charge with a comment."
Democrats on Capitol Hill blasted Trump.
Rep. Adam Schiff, the top Democrat on the House intelligence committee, said that if Trump is going to accuse Rice of a crime, he should make the intelligence public.
"If he's going to make accusations of criminality of anyone, he needs to show evidence to support that kind of a charge," Schiff said. "Obviously, that's not something he was either able or willing to do with respect to his accusations against Obama. It's not something I suspect he's going to be able to do with Susan Rice either."
Rep. Eric Swalwell, a California Democrat on the intelligence panel, said he views the allegation as an attempt to divert attention from the ongoing probe into Russian contacts.
"I don't expect they will (declassify) because I think this is just more obstruction," Swalwell said. "If he has evidence that she committed a crime, he actually can show us what his evidence is. Right now he has a credibility problem because he's been proved wrong a lot. ... This seems nothing more than buying time and obstructionism."
Trump did not repeat his claim at a White House news conference shortly after the Times interview.