The New York Times put out a statement Sunday detailing an initially off-the-record meeting the paper's publisher had with President Donald Trump on July 20.

The paper said it was choosing to divulge those details after Trump tweeted about the meeting Sunday morning, thereby putting it on the record.

Trump said he had a "good and interesting meeting" with The Times' publisher, A.G. Sulzberger, adding that they spent 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.'"

In a statement, Sulzberger said the White House requested the meeting and that he accepted the invitation so he could warn the president about the danger of his "deeply troubling anti-press rhetoric."

The New York Times put out a statement Sunday that sought to counter President Donald Trump's claim earlier in the day about a meeting with A.G. Sulzberger, the paper's publisher.

"Had a very good and interesting meeting at the White House with A.G. Sulzberger, Publisher of the New York Times," the president tweeted on Sunday morning. "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!"

Trump frequently employs the term "fake news" to describe unfavorable press coverage, and the phrase "enemy of the people" gained traction when Trump used it last year, shortly after taking office, to criticize coverage he did not like.

Later Sunday, The Times released a statement saying the White House had requested the meeting, which took place July 20, and asked that it be off the record.

But the paper said Trump's tweet put the meeting on the record, prompting Sulzberger to speak out about its content based on "detailed notes" taken by him and James Bennet, who oversees The Times' editorial page.

Sulzberger said the main reason he accepted Trump's invitation to meet was to "raise concerns about the president's deeply troubling anti-press rhetoric," which he characterized as "divisive" and "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,'" Sulzberger's statement said. "I warned that this inflammatory language is contributing to a rise in threats against journalists and will lead to violence."

Sulzberger also said he emphasized during the meeting that he was not asking the president to soften his attacks on The Times if he felt the paper's coverage was unfair.

"Instead, I implored him to reconsider his broader attacks on journalism, which I believe are dangerous and harmful to our country," the statement concluded.

The Times is a frequent target for Trump, who often dubs the paper "the Failing New York Times," though it has reported consistently rising subscriptions and readership figures since Trump took office.

In a series of tweets after The Times released Sulzberger's statement, Trump attempted to spin Sulzberger's words to suggest it was media outlets that were 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!" the president tweeted. "Very unpatriotic! Freedom of the press also comes with a responsibility to report the news accurately."

He added: "90% of media coverage of my Administration is negative, despite the tremendously positive results we are achieving, it's no surprise that confidence in the media is at an all time low! I will not allow our great country to be sold out by anti-Trump haters in the dying newspaper industry.

"No matter how much they try to distract and cover it up, our country is making great progress under my leadership and I will never stop fighting for the American people!" he continued. "As an example, the failing New York Times and the Amazon Washington Post do nothing but write bad stories even on very positive achievements — and they will never change!"

Earlier in the week, the White House drew sharp scrutiny when it barred the CNN reporter Kaitlan Collins from a Rose Garden press event after she asked Trump tough questions about Michael Cohen and the president's summit in Helsinki with Russian President Vladimir Putin two weeks ago.

Trump and his allies frequently insult reporters such as CNN's Jim Acosta, and the daily press briefings often feature contentious back-and-forths between reporters and the White House press secretary, Sarah Huckabee Sanders.

As Sulzberger noted, it's not uncommon for the White House and the press to have a tense relationship. But observers have said the Trump White House's relationship with news outlets appears to be at a particularly low point in large part because of Trump's tendency to deem coverage he doesn't like as "fake" or "dishonest."

Sulzberger took over as publisher from his father, Arthur Ochs Sulzberger Jr., in January, more than a year after Trump met with Times editors and reporters for a wide-ranging interview after his 2016 election victory.