The offending clip is an altered version of Donald Trump's appearance at a World Wrestling Entertainment event in 2007, long before he became United States president.
In the new, doctored video, he wrestles a man with CNN superimposed on his head to the ground, then throws punches at the man's head before walking away.
CNN has responded by calling it an incitement to violence against the media.
But Donald Trump's homeland security adviser, Thomas Bossert, says no-one would reasonably perceive it that way.
"There's a lot of cable news shows that reach directly into hundreds of thousands of viewers, and they're really not always very fair to the President. So I'm pretty proud of the President for developing a Twitter and a social-media platform where he can talk directly to the American people. In fact, he's the most genuine president, the most non-politician president, that we've seen in my lifetime, and he's demonstrated, whatever the content of that tweet is, or any tweet, he's demonstrated a genuine ability to communicate to the people."
President Trump has long had an antagonistic relationship with CNN, accusing it of being fake news and calling it the Clinton News Network after election rival Hillary Clinton.
He added two hashtags to the new video, #FraudNewsCNN and #FNN.
The video has triggered a backlash on social media, where he has been accused of behaviour not befitting a president.
Lawmakers, especially Democrats, are among those responding, calling it a new low and a threat to both the presidency and the democracy.
But before Mr Trump posted the tweet, he was already making his latest views on the media clear during a speech at an evangelical event honouring veterans in Washington.
"The fake media is trying to silence us, but we will not let them, because the people know the truth. The fake media tried to stop us from going to the White House, but I'm president and they're not."
Meanwhile, protesters have gathered in Chicago calling for Donald Trump to be impeached.
The marches were organised through social media, and demonstrators offered a wide range of issues regarding why they disagreed with the President.
This protester says Mr Trump sets a bad example for others.
"The worst part about this man is his behaviour, the example he sets and the terrible behaviour he encourages. That's why we must get rid of him."
Other protests were planned in Los Angeles and Atlanta.
Share
