"Do I think? Yes, I think," Trump told The New York Times in an interview in the Oval Office, while declining to give evidence or say if he viewed intelligence to back his claim.
He was unclear what crime specifically he is accusing her of committing.
"I think it's going to be the biggest story," Trump said. "It's such an important story for our country and the world. It is one of the big stories of our time."
In a statement today, a spokesperson for Rice, Erin Pelton, said, "I'm not going to dignify the president's ludicrous charge with a comment."
Rice previously called allegations that she requested the unmasking of Trump campaign and transition members for political reasons "absolutely false."
Her position as national security adviser allowed her to request the unmasking, or the identifying of American citizens, in intelligence reports.
"There were occasions when I would receive a report in which a U.S. person was referred to — name not provided, just 'U.S. person.' And sometimes, in that context, in order to understand the importance of the report and assess its significance, it was necessary to find out or request the information as to who the U.S. official was," she said in an interview with MSNBC yesterday afternoon.
"The intelligence community made the determination as to whether or not the identity of that American individual could be provided to me," she added.
Leaking classified information can be a criminal offense, which Rice denied doing. "I leaked nothing to nobody," she told MSNBC.
Last month, House Intelligence Committee Chairman Devin Nunes, R-Calif., made waves when he announced that the communications of Trump transition team members were "incidentally" swept up by U.S. intelligence agencies while they were conducting legal foreign surveillance.
Nunes also said he confirmed that "additional names of Trump transition team members were unmasked."
Trump took Nunes' findings as vindication of his allegations that Obama ordered the wiretapping of Trump Tower in New York during the presidential campaign, a claim that FBI Director James Comey and others said they have no evidence to support.
The White House and Trump later said that the wiretapping allegations referred to broader surveillance by the Obama administration.