Donald Trump on Friday urged his attorney general to investigate the anonymous author of a damning op-ed, escalating his long-running battles with the media and highlighting his suspicions that people are seeking to overthrow his presidency.

Trump, battling one of the deepest crises in his 20-month presidency, has raged about Wednesday's searing essay, branding its unidentified writer a "gutless" coward and accusing The New York Times of borderline treason for publishing it.

"I would say Jeff (Sessions) should be investigating who the author of that piece was because I really believe it's national security," Trump told reporters traveling with him in North Dakota.

"The Times should never have done that, because really what they've done is virtually, you know, it's treason," the president said in an interview with Fox News broadcast earlier Friday.

Asked on Air Force One whether action should be taken against the Times, Trump said "I'm looking at that right now."

Trump appeared to be calling for a criminal investigation despite there being no indication that the mystery author broke any laws by releasing his extraordinary column, which detailed how "unsung heroes" were quietly working within the administration to frustrate an amoral president's "worst inclinations."