President Trump says that President Obama's national security adviser Susan Rice may have committed a crime by unmasking names of Trump associates in US intelligence reports collected by intelligence agencies.
Trump did not repeat his claim at a White House news conference shortly after the Times interview.
Trump and his allies have focused on unsubstantiated reports that Rice, who served as Obama's national security adviser, disclosed the names of Trump aides swept up in USA surveillance of foreign targets.
The Republican chairman of the House Intelligence Committee, Devin Nunes of California, revealed last month that Trump and his campaign aides might have been swept up in USA surveillance of foreign targets during the presidential election.
Trump says in the interview he thinks the Susan Rice allegations will be "one of the big stories of our time".
Rice said through a spokeswoman that she would not dignify "the president's ludicrous charge with a comment". But Rice maintained she is not the leaker, didn't send the information to the press and did not use the information for political purposes.
"If there is intelligence that leads to a reason for us to look at Susan Rice, then we'll do it", Burr told reporters.
In an interview on Tuesday, Rice denied the allegations.
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"I think it's going to be the biggest story", he said.
Nunes said during a March 22 press conference that he was "troubled" because the reports he'd seen were not connected to Russian Federation or any foreign intelligence. The rules specify that in most cases a "generic term", such as "U.S. Person 1" is used, instead of the actual name.
The White House and Trump himself later said that the wiretapping allegations referred to broader surveillance by the Obama administration.
Rep. Peter King, a Republican who sits on the House Intelligence Committee, told Fox that the intelligence reports Americans got swept up in are more detailed than previously thought.
"I have the greatest amount of sympathy, I can't see those pictures, it's heartrending to see those pictures", he said.
Such requests, which a number of senior officials are authorized to make, trigger a legal and intelligence review by the agency to determine whether revealing the name has potential intelligence value and could expose a security threat to the United States, said one of the officials, who is familiar with the process and spoke on condition of anonymity to discuss internal intelligence procedures. Following Nixon's resignation, the intelligence community was reformed via the Foreign Intelligence Surveillance Act, with the hopes of imposing accountability measures for federal officials that spy on political opponents.
Majority members on the House and Senate committees could call Rice, or other people from her era, to testify as Democrats seek Trump campaign aides. Nunes has said he will not step down from his position as chair of the House Intelligence Committee.