The network’s chief White House correspondent was reporting from a Trump rally in Florida when his crew filmed a crowd of the President’s supporters hurling abuse at them.
Various people can be heard screaming “stop lying”, “tell the truth” and “you suck” while making rude gestures at the camera.
Acosta tweeted the video, adding: “Just a sample of the sad scene we faced at the Trump rally in Tampa.
“I’m very worried that the hostility whipped up by Trump and some in conservative media will result in somebody getting hurt.”
He continued: “We should not treat our fellow Americans this way. The press is not the enemy.”
Other footage of the event was shared by Trump’s son, Eric, who chose to add the hastag #Truth. It was later retweeted by the President himself.
The clip prompted criticism from many who viewed it, including former White House communications director, Anthony Scaramucci.
Trump’s rhetoric towards the press has become increasingly belligerent since he took office. At a rally in Kansas last week, the President told the crowd not to “believe the crap you see from these people, the fake news”.
He added: “Just remember, what you are seeing and what you are reading is not what’s happening.”
Earlier this week the publisher of The New York Times, AG Sulzberger, was forced to issue a statement after Trump tweeted about an off-the-record meeting between the two.
He said: “My main purpose for accepting the meeting was to raise concerns about the president’s deeply troubling anti-press rhetoric.
“I told the president directly that I thought that his language was not just divisive but 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 added.
“I warned that this inflammatory language is contributing to a rise in threats against journalists and will lead to violence.”
Both Trump and his supporters appear happy to ignore the well-documented fact he has lied over 3,200 times since taking office.
The rally speech in Tampa on Tuesday contained many elements that have become commonplace at his political events. Several hecklers were ejected, while Trump attacked public opinion polls, except one that said he was popular among Republicans.
The President, in Florida to campaign for Republican governor Rick Scott’s bid for a US Senate seat and US representative Ron DeSantis’ campaign for governor, also said he could tame his raucous presidential style if he wanted.
“I can be more presidential than any president in history except for maybe Abe Lincoln with the big hat,” Trump said. “I admit it, Abe Lincoln is tough.”