The US administration revoked Mr Acosta's access last week following President Donald Trump's controversial post-election news conference, where Mr Acosta refused to give up a microphone when the president said he did not want to hear anything more from him.
Without his press credentials, Acosta's ability to perform his job as White House correspondent "is effectively eliminated", CNN said in its lawsuit. When the exchange became tense, Trump said, "That's enough", and the CNN journalist struggled with a White House intern for the microphone. CEO Jeff Zucker, in a letter to White House chief of staff John Kelly, called it a "pattern of targeted harassment".
CNN said Acosta was given no warning of the action, and no recourse to appeal it. Acosta traveled to Paris to cover Trump's visit there this weekend and, although given permission by the French government to cover a news event, the Secret Service denied him entrance, the company said. "You ask a lot of stupid questions".
The comments followed Trump's attacks during the same question and answer session on CNN reporter Jim Acosta, who he called "unprofessional" and not smart, and Urban Radio Networks' April Ryan, who he called "very nasty" and "a loser". The lawsuit demands the reinstatement of Acosta's press credentials. "If left unchallenged, the actions of the White House could create a unsafe chilling effect for any journalist who covers our elected officials".
The video in question has come under mass scrutiny as it appears to be a sped-up version of original footage that was altered to make Acosta's actions look more aggressive towards the White House intern as she yanks down on his microphone.
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However, Ms Roney said a bail application would not be considered until more information about the case was known. No injuries were reported from the needles, but the recall extended to six states as well as New Zealand.
The White House did not respond to multiple queries about the origin of the video.
And he said it again on Friday, two days after blacklisting Acosta.
He also said he was "not a great fan" of Trump's.
Other CNN reporters and producers continue to work from the White House grounds, but not Acosta.
Another added: "This is a new low even for you".
"This sort of angry, irrational, false, arbitrary, capricious content-based discrimination regarding a White House press credential against a journalist quite clearly violates the First Amendment", he wrote. The agency said Sherrill, who had been in a fistfight with one of Johnson's campaign aides, was a physical threat to the president. "We can't have the White House tossing people out because they don't like what they are saying or what they are reporting".