On Twitter, in a Fox News interview and again at a campaign rally in Billings, Montana, the US president mistakenly suggested the article was a treasonous act.
High-ranking members of the administration have raced to distance themselves from the article, which paints a picture of a White House in chaos where officials deliberately work to thwart the president’s most dangerous impulses.
Mr Trump told the Montana rally on Thursday night that “unelected deep state operatives” are a “threat to democracy itself”.
He suggested the person who wrote the op-ed “may not be a Republican, it may not be a conservative, it may be a deep state person who has been there for a long time”.
He claimed erroneously in a Fox interview before the rally that "what they've done is virtually, you know, it's treason, you could call it a lot of things."
And he told supporters afterwards: “Is it subversion? Is it treason? It's a horrible thing.”
Treason has a very specific legal definition in the US constitution, relating to acts that aid countries with whom America is actively at war - or to an American citizen mustering for military action against the US themselves.
At the same time as calling the article treasonous, though, Mr Trump claimed he “didn’t mind”.
“I don't mind when they write books and they write lies because they get discredited,” he told Fox.
He said the New York Times’ decision to publish the anonymous article was “really sad for the mainstream media”, and one that has “backfired” as he has “picked up a lot of support” as a result.
The unsigned opinion piece has so far drawn disavowals from at least 11 top advisers to the president, including Vice President Mike Pence, Ambassador to Russia Jon Huntsman, Secretary of State Mike Pompeo and Defense Secretary James Mattis, all of whom denied any responsibility for its authorship.
Published on Wednesday, the column appeared days after the release of excerpts from a book by famed reporter Bob Woodward that portrayed Mr Trump as prone to impulsive decision-making. The excerpts said aides sometimes tried to limit what they saw as damaging behaviour by disregarding his instructions.
The Times op-ed, and Woodward's book, which is to be published next week, followed many news articles during Mr Trump's 19-month presidency that have depicted turbulence inside the White House under his leadership.
Additional reporting by agencies
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