Some of Trump's supporters say Rice's actions prove the president's previous claims that he was wiretapped at Trump Tower by the Obama administration.
Sen. Rand Paul (R-KY) is calling for former National Security Advisor Susan Rice to "testify under oath" after reports broke indicating that she used her power to spy on President Trump's associates during campaign season.
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.
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.
Rice reportedly asked to unmask the identities of people affiliated with the Trump campaign and transition "on dozens of occasions", according to the Bloomberg report.
Republicans do not call it "outrageous" that Rice might have been involved in potentially asking for Americans to be "unmasked" in classified reports about legal surveillance of foreign targets - including potentially of Trump or his aides.
"I leaked nothing to nobody, and never have and never would", Rice told MSNBC.
Trump himself said Wednesday that he believes Rice may have committed a crime. Rice denied this allegation during her MSNBC interview.
"I think it's going to be the biggest story", the president said.
It was Nunes who first raised the unmasking allegations, saying that some names were unmasked in the documents he reviewed. The president repeatedly refused attempts of the two reporters of New York Times who wished to know what led him to this conclusion, though the President said he would talk more "at the right time". James Comey testified on March 20 that neither the Federal Bureau of Investigation nor the Department of Justice have found any evidence of Obama and his administration wiretapping Trump Tower.
The House and Senate Intelligence Committees are now investigating allegations the Obama administration spied on Trump associates - and possibly Trump himself - for as long as the year preceding his inauguration. "I leaked nothing to nobody, and never have and never would", Rice said. If Rice asked for names to be unmasked, those would have been lower level officials or those without specific titles. "She should not have time to be unmasking individuals having conversations".
The Trump associates, who were incidentally mentioned on intercepted communications during the Obama administration, were not under surveillance themselves, but had been recorded while speaking with foreigners who were under surveillance by the US.
"Our requests are simply not being answered", said one House Intelligence committee source about the lack of responsiveness. And in the Senate, both Warner and Senate Intelligence Committee Chairman Richard Burr of North Carolina said they thought it was appropriate.