The publisher of The New York Times has responded to a tweet from Donald Trump in which he claimed the two discussed the “vast amount of fake news being put out by the media” during a recent meeting at the White House.

AG Sulzberger published a note detailing the conversation he had with Mr Trump, saying he repeatedly urged the US president to reconsider his attacks on the media.

Mr Sulzberger said the meeting had originally been off-the-record per the White House's request, but that the president's public comment on the issue had negated that request.

“My main purpose for accepting the meeting was to raise concerns about the president’s deeply troubling anti-press rhetoric,” Mr Sulzberger wrote. “I told the president directly that I thought that his language was not just divisive but increasingly dangerous.”

He continued: “I told him that although the phrase ‘fake news’ is untrue and harmful, I am far more concerned about his labelling 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.”

AG Sulzberger poses for a photo on the 16th floor of the New York Times building in New York (AP)

Mr Trump had tweeted earlier in the day that he had had an “interesting” conversation with the publisher of the storied American newspaper.

“Had a very good and interesting meeting at the White House with AG Sulzberger, Publisher of the New York Times,” Mr Trump’s tweet read. “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!”

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Mr Sulzberger, in his note, said the implications of that sort of language – and the verbal attacks – was even more damning for countries with less press freedoms than are enjoyed by journalists in the US.

“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,” Mr Sulzberger wrote. “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.”

Later Sunday, Mr Trump tweeted an attack, seeming to say that reporting on deliberations of the Trump administration — a common practice for journalists to do with all presidential administrations when information becomes available to reporters — is putting lives at risk.

"When the media - driven insane by their Trump Derangement Syndrome - reveals internal deliberations of our government, it truly puts the lives of many, not just journalists, at risk! Very unpatriotic! Freedom of the press also comes with a responsibility to report the news..." he wrote.

Mr Trump has repeatedly attacked the media during his time as president, painting most outlets as purveyors of “fake news” – though he does not generally provide citation for those claims.