In response, the news network has called for another an emergency court hearing claiming the Trump administration is continuing to breach the constitutional rights of the First Amendment - free speech - and the Fifth Amendment, the right to due process.
On Friday, District Judge Timothy Kelly temporarily restored Acosta's credentials for 14 days, saying the White House had failed to provide due process in removing Mr Acosta's pass over "inappropriate" behaviour at a press conference where he clashed with Donald Trump .
The judge did not address any alleged violations of free speech, which will form part of the arguments in CNN's larger lawsuit over the move.
In a letter later on Friday, Press Secretary Sarah Huckabee Sanders and Communications Director Bill Shine sent Mr Acosta a letter stating the White House made a "preliminary decision" to revoke his pass once the order expired on 30 November.
In a filing on Monday, CNN and Mr Acosta asked for an expedited hearing next week.
“The White House is continuing to violate the First and 5th Amendments of the Constitution,” the network said in a statement. “These actions threaten all journalists and news organisations. Jim Acosta and CNN will continue to report the news about the White House and the president.”
The White House opposed the request for an emergency hearing, writing in response to the court: “Not only is there no 'emergency' right now, it is impossible to know at this point whether next steps are necessary, much less what those steps should be.”
It said the White House expected to make its final decision on Mr Acosta credentials by 3pm on Friday.
Mr Acosta had been accused by the White House of getting physical with a press intern during a particularly tense 7 November exchange with the president as the young woman attempted to take the microphone back from the reporter.
At the time, Ms Sanders tweeted out what appeared to be a doctored video, edited to show Mr Acosta pushing the woman’s arm away.
“We will not tolerate the inappropriate behaviour clearly documented in this video,” she tweeted. The White House later appeared to drop that claim, merely saying that Mr Acosta had acted inappropriately in refusing to give up the microphone and trying to ask multiple questions.
Mr Trump told Fox News on Sunday would have his pass pulled if he “misbehaves” again; “we’ll throw him out,” he added.
Mr Trump said the court ruling issued late last week to reinstate Mr Acosta’s access was “not a big deal,” adding “what they said, though, is that we have to create rules and regulations for conduct etc. etc. We’re doing that, were going to write them up right now”.
Ms Sanders responded in a statement after the court's initial ruling on Friday that the White House will "further develop rules and processes to ensure fair and orderly press conferences in the future."
CNN has been vocal in their defence of all journalists’ access to report from the White House.
Mr Trump has frequently hit out at the network, calling it “fake news” and “truly dishonest...sick people”. His exchange with Mr Acosta was not an isolated incident. The president called several questions from female, African-American journalists in the White House press corps "stupid" and "racist" at various points that same week.
The news network was also the recipient of two packages with explosive devices, addressed to former Director of National Intelligence James Clapper and former CIA Director John Brennan - just two of a string of explosives sent to several prominent Democrats in recent weeks who were all vocal critics of Mr Trump.