The president said CNN's journalist was "unfortunate, a terrible person" at the press event.
Mr Acosta challenged Mr Trump's recent inquiries for a migrant caravan heading to the US from Central A
"That's enough, that's enough," said the president to Mr Acosta, before saying he sat down and put the best to his / her microphone.
"CNN should be ashamed of themselves, after you have worked for them," he said. "The way you're treating Sarah Huckabee [Sanders] terrible. "
What did the White House say?
Ms Sanders stated in a statement issued in Twitter threads that "White House" would never tolerate a correspondent putting his hands on a young woman just trying to do her job. "
"The fact that CNN is proud of the way in which their behaved worker is not only disgraceful, he's an incredibly ignored example for everyone, including young women, who works in this Ministry, "he said.
"As a result of today's event, the White House prevents the hard copy of the correspondent in question until further notice."
Later, the press secretary wrote a glip to zoom out of the event, saying they "will not tolerate the inappropriate behavior that is clearly documented in this video".
Mr Acosta posted a tweet saying he had been suspended by the Secret Service from entering the White House land.
What was the reaction?
Journalists started the move to abolish Mr Acosta's access.
CNN announced a statement on Twitter saying that the ban was "backup for [Jim Acosta’s] challenging questions ".
"In an explanation, said Press Secretary, Sarah Sanders," he said. "He gave fraudulent allegations who indicated an incident that had never happened."
The White House Correspondents' Association – a group that represents the press body in the presidential residence – of the name "outside the line" and "unacceptable".
"We're urging the White House to reverse the weak act and this error straight away." And Chronicle.