On Sunday, CNN responded to the president's latest tweet.
"Hope you are enjoying #4thofjulyweekend and celebrating our cherished #1A freedoms enshrined in our Constitution which can not be taken away", he wrote on his private account, referring to the First Amendment.
The video appeared to be a modified version of a 2007 appearance by Mr Trump at World Wrestling Entertainment's WrestleMania 23 promotion, in which Mr Trump "takes down" WWE chairman Vince McMahon - in Sunday's video, McMahon's head has been replaced with the CNN logo.
He has always been critical of the American network, which he has repeatedly accused of broadcasting "fake news" about his presidency.
She also criticized Trump's homeland security adviser Tom Bossert, who had earlier defended Trump on the network, claiming the president is attacked by the media. "Thank you Mr. President Trump we do not deserve you", added another. It's one of those appearances that wrestling fans never forget, although I'm sure a good portion of them have tried to selectively remove it from their memory.
Meanwhile, the CNN communications team tweeted a seemingly sarcastic response quoting White House press officer Sarah Huckabee Sanders, who said on Thursday: "The President in no way form or fashion has ever promoted or encouraged violence. I hope they don't", he said.
"He's beaten up, in a way, on the cable platforms - he has a right to respond", Bossert said. Many joined the conversation to tell Trump their views about whether wrestling memes were an appropriate way for a U.S. President to comport himself.
McEnany made it clear that she wouldn't have advised Trump to tweet out that video, but she also said, "I think it was intended as a tongue-in-cheek, satirical video".
After the president's tweets, Reddit users expressed disbelief at the president's use of the clip. "He should start doing his", they concluded.
For days, Trump has focused his ire on Brzezinski and Joe Scarborough, co-hosts of MSNBC's "Morning Joe".
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