"It's national security", the president said on Air Force One, on the way to a rally in North Dakota Friday.
"We're going to take a look at what he had, what he gave, what he's talking about, also where he is right now", Trump replied.
"This could be very risky if the person who is talking to the media is actually revealing national security secrets", he added.
Following the op-ed's publication Wednesday, a long list of senior Trump administration officials have come out publicly to deny they are behind it, including Vice President Mike Pence.
In his own piece, McCarthy describes the anonymous op-ed as "shocking", albeit unsurprising as a "permanent political class" desperately attempts to regain its waning power in the Trump era. His administration went into a complete meltdown after a bombshell op-ed. "I mean it was the weakest economic recovery since the Great Depression", Pence said. Trump says it was unfair for the person to pen the editorial because there's no way to discredit it.More news: NAFTA talks make progress; U.S., Canadian officials to work into night
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Asked to comment, Justice Department press secretary Sarah Isgur Flores said the "department does not confirm or deny investigations".
"People think that it is disgusting that the New York Times would do that".
Republican Sen. Rand Paul of Kentucky told reporters Thursday that he thinks any White House employee with a security clearance should undergo a lie detector test to determine who wrote it.
"If the GUTLESS anonymous person does indeed exist, The Times must, for National Security purposes, turn him/her over to the government at once", the president added.
In the piece, the author, whose identity the Times is withholding, wrote "I work for the president but like-minded colleagues and I have vowed to thwart parts of his agenda and his worst inclinations".
Meanwhile, a string of Mr Trump's most senior cabinet members have denied responsibility for the explosive account of how his own team was trying to frustrate the USA president's wishes. Friday night, Trump asked the state's two senators - Mike Rounds and John Thune - to change libel laws to avoid unfavorable coverage. "That's not hypothetical", said the former president.