On Tuesday, the newspaper was forced to change its front-page headline over its portrayal of Mr Trump’s speech following the attacks in Texas and Ohio which left 31 people dead.
The first headline read, “TRUMP URGES UNITY VS RACISM”, but was changed to, “ASSAILING HATE BUT NOT GUNS” following outrage as the portrayal of the US president as a unifier.
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“’Trump Urges Unity Vs. Racism,’ was the correct description in the first headline by the Failing New York Times, but it was quickly changed to, ‘Assailing Hate But Not Guns,’ after the Radical Left Democrats went absolutely CRAZY! Fake News,” Mr Trump tweeted early on Wednesday morning.
The president then tweeted a quote from Mark Penn, a marketing executive and former adviser to Bill and Hillary Clinton, who had appeared on Fox News to discuss the headline change.
“’That’s what we’re up against. This is an astounding development in journalism. I’ve never seen it happen before, I’ve just never seen anything like this! Is that journalism today? I don’t think so!’ Mark Penn, Former Clinton Advisor,” Mr Trump tweeted.
He added: “After 3 years I almost got a good headline from the Times!”
The NYT’s headline for their first edition of Tuesday’s paper was picked up on by the author and statistician Nate Silver, who tweeted an image of the front page. “Not sure “TRUMP URGES UNITY VS. RACISM” is how I would have framed the story,” he wrote.
It prompted a flurry of criticism from left-leaning politicians and a new debate over how such tragedies should be covered, with Democrat congresswoman Alexandria Ocasio-Cortez commenting that the newspaper’s interpretation of events over the weekend – when 31 were killed in two separate gun attacks – was a reminder that “white supremacy is aided by – and often relies upon – the cowardice of mainstream institutions”.
Democratic presidential contender Beto O’Rourke called it “unbelievable” while New York City’s mayor, Bill de Blasio, questioned the paper’s tagline: ”The truth is worth it.” He wrote: “Not the truth. Not worth it.”
In a later tweet on Wednesday morning Mr Trump followed his aides in seeking to draw links between the Dayton, Ohio shooter and his alleged support for “political figures like Bernie Sanders, Elizabeth Warren”.
Mr Trump said: “I hope other news outlets will report this as opposed to Fake News. Thank you!”
White House aide Kellyanne Conway had appeared on Fox News on Tuesday in an attempt to shift the narrative away from one which drew any lines between Mr Trump’s racist rhetoric and the alleged El Paso gunman, whose online manifesto was filled with white supremacist language and hatred aimed at immigrants.
“It looks like this Dayton monster, the shooter in Ohio, had leftist leanings and a Twitter feed that was complimentary of antifa, complimentary of Elizabeth Warren and Bernie Sanders,” she said. “Am I blaming them for the shooting? Of course not.”
Dayton police chief Richard Biehl said there was no evidence of ”bias motive” and officers were still investigating any triggers for the killing.