On Wednesday, The New York Times published an op-ed from an anonymous "senior official" in the Trump administration titled "I Am Part of the Resistance Inside the Trump Administration".
Mr Trump hit back via Twitter and during a campaign rally at the 12,000-seat Rimrock Auto Arena in Billings, Montana, on Thursday evening.
"We have reached an all-time low", he told the crowd.
He said it was a "disgrace" for the newspaper to have published the op-ed from a purported senior administration official.
There have been a series of denials from Trump's closest aides over the weekend, with vice president Mike Pence and counselor Kellyanne Conway being among those who have categorically denied writing the New York Times op-ed.More news: Eye of Hurricane Olivia breaking apart
"The President's threats both underscore why we must safeguard the identity of the writer of this op-ed and serve as a reminder of the importance of a free and independent press to American democracy".
Trump has called the forthcoming book "total fiction - just like he wrote in the past about other presidents". "The Dems are going insane!"
The essay said members of the administration were running a "two-track presidency", achieving Republican policy aims while sidelining the "amoral ... impetuous, adversarial, petty and ineffective" Trump until he was out of office. "This coward should do the right thing and resign".
WASHINGTON-President Donald Trump said Friday his Justice Department should launch an investigation into what government official penned an anonymous New York Times Op-Edis job.
Some Trump administration officials and allies claim the author could have hindered national security by giving USA foes and friends alike the sense there is a weak and unfit commander in chief in the Oval Office.More news: Fairytale ends but surge whets Millman’s appetite for big time
Independent voters and those who voted grudgingly for Mr Trump in 2016 may pause, Dr Bullock said. But "for Democrats, it confirms their worst suspicions".
Like the "Deep State" itself, the origins of the term are shrouded in mystery. "I think it's national security - I would say Jeff should be investigating who the author of that piece was because I really believe it's national security", the president said of the matter.
"It's created to depress the turnout of the President's base so that the Democrats will win the House of Representatives".
"We have a seemingly endless stream of stories about a White House that is at war with itself and a White House staff who are at war with the President", Dr Altschuler said.
The president noted that all of the top administration officials have already denied authorship of the letter.More news: Myanmar rejects int’l court’s right to Rohingya probe