"No, they won't. The President can't decree it, no court is going to enforce it".
Trump said on Friday that he's called on the U.S. Justice Department to investigate the Times after the op-ed.
Trump regularly attacks the media for focusing on negative news about his administration and decries what he perceives as 'fakes news.' He repeated on Air Force One that he believes libel laws should be strengthened.
Trump, meanwhile, publicly raged against the author and the newspaper, calling the anonymous official "gutless" while also suggesting the person may not exist at all. Still, writing unflattering things about the president isn't a crime.
The information isn't available from any other source.
"It should not be a partisan issue to say that we do not pressure the attorney general or the Federal Bureau of Investigation to use the criminal justice system as a cudgel to punish our political opponents", added Mr Obama.
When news organizations use an unnamed source, they are asking readers to trust the credibility of the information at a time of public distrust in the media. "I would say Jeff [Sessions] should be investigating the author because it's national security". If the person has a high-level security clearance, he said, "I don't want him in those meetings".
Still Trump's call is the latest test of the independence of his Justice Department, which is supposed to make investigative and charging decisions without political interference from the White House.
"For the sake of our national security, the New York Times should publish his name at once".
"Whereas right now we're talking about the substance of what's in the op-ed", he said.
"People talk about the loyalists leaving", the person close to Trump said.
"I do, I do", he said.
"He goes into a high level meeting concerning China or Russian Federation or North Korea or something, I don't want him in those meetings", he said. It said the senior administration official's job would be jeopardized by its disclosure.
Mr Trump described the writer as "gutless" and the newspaper as "phony".
The column has set off a wild guessing game on the author's identity.