Acosta accused the president of attempting to frighten voters ahead of the midterms with ads depicting the migrant caravan as invaders.
As the reporter continued, Mr Trump declared: "That's enough, put down the mic" and walked away from his own podium, as if leaving. "I'm sick of him being the story, I'm sick of talking about Jim Acosta", she said.
Acosta called the White House's claims "lies" and CNN defended its reporter in a statement.
In an official statement, CNN said that "Press Secretary Sarah Sanders lied".
The president had been talking to other reporters and really railing against them. Sanders said on Twitter that the White House would "never tolerate a reporter placing his hands on a young woman just trying to do her job as a White House intern", though no video evidence has so far supported that claim. "This conduct is absolutely unacceptable", she wrote. It is also completely disrespectful to the reporter's colleagues not to allow them an opportunity to ask a question.
Former president of the White House Correspondents Association, Jeff Mason, refuted the White House accusation that Acosta placed his hand on a female White House intern.
The New York Times editorialized in favor of restoring Acosta's pass, saying it signaled Trump's view that asking hard questions disqualifies reporters from attending briefings.
"I came in here as a nice person wanting to answer questions, and I had people jumping out of their seats screaming questions at me", Trump said.
Other Twitter users showed Sanders' video side-by-side with the original broadcast to argue the one she posted had been doctored.
"This President's ongoing attacks on the press have gone too far".
The revocation of Acosta's "hard pass" which provides access to the White House grounds is without any precedent in modern history.
So, as the president said that the question was racist, and I - he was literally having white nationalists at the White House. And Acosta has been one of the more visible thorns in the side of the White House.
"I worked with Jim @Acosta at CNN".
In a later tweet, Sanders said the White House stood by its decision.
The activist, Jennicet Gutiérrez, who is transgender and says she is in the country illegally, interrupted Mr. Obama shortly after he began speaking, calling from the back of the room, "President Obama, release all L.G.B.T.Q. immigrants from detention and stop all deportations!"
What did the White House say?
But a review of the video clearly shows that Acosta did not place "his hands on a young woman" ― but, rather, that he moved the mic away from her as she tried to grab it and that his left hand briefly came into contact with the crook of her elbow as he gestured toward the president.
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