Acosta also tweeted a video of a Secret Service official taking his White House credential from him.
CNN have released a statement on the incident and have included their full support for the reporter.
In a series of tweets, Press Secretary Sarah Huckabee Sanders later confirmed the indefinite suspension of Acosta's pass, accusing the reporter of "placing his hands" on a White House intern during Trump's press conference on Wednesday afternoon. "This conduct is absolutely unacceptable", Sanders said.
Acosta has frequently clashed with Sanders during the White House's irregular news briefings and with Trump in televised news conferences.
And CNN has slammed the White House for its actions.
When another journalist tried to speak up in Acosta's defence, Trump told the second reporter: "I'm not a big fan of yours, either".
"We will not tolerate the inappropriate behavior clearly documented in this video", she wrote. I also love the world, and I don't mind helping the world, but we have to straighten out our country first. "But they have to come in legally".
Mr Acosta pointed out the migrant caravan was "hundreds of miles" away from the United States border. "That is not an invasion".
"CNN should be ashamed of themselves, having you work for them", he said.
"You run CNN. And if you did it well, your ratings will be much higher". Instead, Acosta continued with a second question about the Russian investigation, which Trump shrugged off with another curt answer. He said Acosta held on to the microphone as the intern reached for it and later posted a few pictures from the press conference to prove his point. Waving his finger, Trump berated him. As I told the officer, I don't blame him.
'I think you should let me run the country and you run CNN, ' he snapped. You are a rude bad person. "What do you say to that?"
The incident in question happened during a tense exchange between Acosta and Trump.
"They can play that game, but we can play it better", he said.
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