Trump, who met Sulzberger recently at the White House, tweeted: "Had a very good and interesting meeting at the White House with A.G. Sulzberger, Publisher of the New York Times. Spent much time talking about the vast amounts of Fake News being put out by the media & how that Fake News has morphed into phrase, “Enemy of the People.” Sad!"

In reply, the NYT publisher said in a statement: "...I am far more concerned about his labeling journalists “the enemy of the people.” I warned that this inflammatory language is contributing to a rise in threats against journalists and will lead to violence."

Sulzberger said that the President had every right to voice his opinion if he felt that the coverage wasn't right, but told him to reconsider his usage of words.

"I made clear repeatedly that I was not asking for him to soften his attacks on The Times if he felt our coverage was unfair. Instead, I implored him to reconsider his broader attacks on journalism, which I believe are dangerous and harmful to our country."

Ever since taking office, Trump has been labelling most stories against him as 'fake'.

Here's Sulzberger's full statement

My main purpose for accepting the meeting was to raise concerns about the president’s deeply troubling anti-press rhetoric.

I told the president directly that I thought that his language was not just divisive but increasingly dangerous.

I told him that although the phrase “fake news” is untrue and harmful, I am far more concerned about his labeling journalists “the enemy of the people.” I warned that this inflammatory language is contributing to a rise in threats against journalists and will lead to violence.

I repeatedly stressed that this is particularly true abroad, where the president’s rhetoric is being used by some regimes to justify sweeping crackdowns on journalists. I warned that it was putting lives at risk, that it was undermining the democratic ideals of our nation, and that it was eroding one of our country’s greatest exports: a commitment to free speech and a free press.

Throughout the conversation I emphasized that if President Trump, like previous presidents, was upset with coverage of his administration he was of course free to tell the world. I made clear repeatedly that I was not asking for him to soften his attacks on The Times if he felt our coverage was unfair. Instead, I implored him to reconsider his broader attacks on journalism, which I believe are dangerous and harmful to our country.