Mr Trump tweeted a video of himself during a 2007 World Wrestling Entertainment (WWE) appearance during which he play-fights a man in a suit, only in the video the man's face is replaced by a CNN logo.
He tweeted it from his personal account and then re-tweeted it on the official @POTUS account, meaning it will be saved to the National Archives as part of the official record of his term.
Mr Trump has made it clear he thinks CNN, several other networks, the New York Times, and Washington Post are all "fake news" - a rallying cry at many of his campaign speeches that has been a mainstay during his term in office.
He branded the network as "#FraudNewsNetwork" in the tweet which has been shared over 300,000 times.
Twitter has an official policy on "abuse" and the social media site reviewed the tweet - which Bruce Brown, executive director of the Reporters Committee for Freedom of the Press, said was “threat of physical violence against journalists...beneath the office of the presidency".
However, it has determined the tweet does not violate any terms and conditions.
Tom Bossert, Homeland Security Adviser, said on ABC that "no one would perceive that as a threat".
"I do think that he’s beaten up in a way on cable platforms that he has a right to respond to,” said Mr Bossert, adding that critics were following a pattern of attacking the President by taking it too seriously.
"He is going to get somebody killed in the media," Republican political commentator Ana Navarro said.
She also pointed out that there are those on the political left who have, in her opinion, incited violence as well. Actor Johnny Depp made a "joke" about someone killing Mr Trump and comedian Kathy Griffin did a photo shoot holding a paper mache, severed, bloody head of the President.
Ms Navarro also said on CNN that those are not a direct comparison because "you cannot compete with the bully pulpit, the power, the reach" of Mr Trump's Twitter presence as the US president.
Mr Trump took to Twitter once again to respond to the several people who condemned his actions, writing:
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