In a filing on Monday, CNN and Acosta asked for an expedited hearing next week after top White House communications officials told Acosta in a letter late on Friday that it had already made a decision to suspend his pass once the two-week restraining order expires.
The White House letter, seeking to address the question of due process, said Acosta "violated basic standards" of news events when he got into a heated exchange with President Donald Trump on November 7.
In a court filing on Monday, CNN's lawyers said the network and Acosta "remain hopeful" that the parties "can resolve this dispute without further court intervention".
In a statement about the letter on Sunday, CNN said: "The White House is continuing to violate the First and Fifth Amendments of the Constitution". In the Friday ruling, Washington, D.C., District Court Judge Timothy Kelly restored Acosta's credentials temporarily while a CNN lawsuit against the administration proceeded. Trump responded by branding Acosta a "rude, bad person". But the White House wasted no time informing Acosta of a "preliminary decision" to suspend his pass after that period is up.
All of this was detailed by CNN in a progress report filed in court on Monday. Late Friday, top officials named as defendants in the suit from CNN and Acosta suggested that the "preliminary" decision to revoke Acosta's pass earlier this month could be final if he doesn't submit materials to argue his case by November 18, for a final decision November 19.
The White House press office on Monday released new "rules" that they claim will allow the suspension of press credentials if a reporter refuses to yield the floor after asking only one question.
According to John Roberts of Fox News and Jonathan Karl of ABC News, the White House plans to abandon its efforts to pull Acosta's credential.
The report says that CNN had meant to "resolve this dispute amicably" by working with the White House and the White House Correspondents' Association "to establish protocols" for press conferences "on a going forward basis".
The drama between the White House and Jim Acosta isn't over yet.
For his part, Trump has said the issue is "not a big deal."
When Wallace asked what rules the administration would put in place as a result of the judge's decision, Trump responded: "We're writing them now".
"And if he misbehaves, we'll throw him out, or we'll stop the news conference", Trump added, referring to Acosta.