He asked Trump why he has characterised it as an invasion.
A White House staff member steps in to try to take the microphone away from Acosta.
"President Trump believes in a free press and expects and welcomes tough questions of him and his Administration", Sanders said in her statement.
There has been much controversy over if Acosta was trying to physically get the woman away from him or if the hand brush was an accidental touch, as the White House used the former accusation to justify taking Acosta's press credentials.
She called Acosta's behavior "absolutely unacceptable".
Acosta was stopped by the Secret Service from entering the White House at about 7 pm.
"In an explanation, Press Secretary Sarah Sanders lied", the network said.
"We will not tolerate the inappropriate behaviour clearly documented in this video", Sanders tweeted.
CNN addressed the decision Wednesday, calling it an "unprecedented decision" based on "lies".
Tinting the video red and playing it over a transparent version of the original showed, Mr Shimunov said, the clip had been "sped up to make Jim Acosta's motion look like a chop".
So, as the president said that the question was racist, and I - he was literally having white nationalists at the White House. "We stand by our statement", Sanders said Thursday morning.
It was the latest in a long history of fiery run-ins between the mercurial Republican leader and Acosta.
They began sparring Wednesday after Acosta asked Trump about the caravan of migrants heading from Latin America to the southern USA border. Maybe they will not come forward and say that, but they say that.
At that point, the president snapped. "I think I'm just covering a story, honestly", Acosta said in a 2017 interview with The Washington Post about his reporting style.
"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", said Trump, who talked for almost 90 minutes despite the run-ins with reporters.
When an intern tried to take the mic from Acosta to let the next reporter ask a question, he continued needling the president, who finally called him a "rude, awful person".
Waving his finger, Mr Trump berated him. "I'm telling you what the law is". Wait. You know why we need the people? "You and I have a difference of opinion", he said.
Stirewalt said that either way, the episode hurts the political discourse as the Acosta-Trump feud overshadowed "a bunch of good questions" from reporters like Fox News' John Roberts and CBS News' Major Garrett.
"Well, I'm not a big fan of yours either", Trump quipped, adding, "You aren't the best".
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