"We want to just simply move forward and let CNN and Jim Acosta gather news and report it," CNN lawyer Ted Boutrous said in an interview on Friday.
He said the law is "very clear in terms of how these things should proceed and what the White House can and can't do."
Boutrous said CNN would welcome a settlement of the lawsuit, now that Judge Timothy J. Kelly has sided with CNN and forced the government to return Acosta's press pass for the time being.
In these situations, Boutrous said, "you look for a resolution that makes the most sense so everyone can get out of court and get back to their work. And that goes for the White House and for the journalists. So we're open to anything."
But Boutrous also said that the network is prepared for a long-term legal fight if need be.
"We're ready to litigate as long as we have to, to protect these First Amendment rights, to ask the court to declare rules of the road going forward," he said.
The government has not formally said what its next step will be. But Trump downplayed the impact of the loss in court, telling Fox's Chris Wallace in an interview later in the day that "it's not a big deal."
CNN and Acosta filed the suit on Tuesday, alleging violations of the First and Fifth Amendments. The six defendants include Trump, chief of staff John Kelly and press secretary Sarah Sanders.
Trump and Sanders both spoke on Friday about setting up rules and regulations about how White House reporters act, potentially as a precursor for removing reporters' press passes in the future.
The Justice Department did not mention that, but a spokeswoman said Friday night, "We are disappointed with the district court's decision. The President has broad authority to regulate access to the White House, including to ensure fair and orderly White House events and press conferences. We look forward to continuing to defend the White House's lawful actions."
Kelly heard oral arguments on Wednesday afternoon and reconvened court on Friday morning.
He granted CNN's request for a temporary restraining order on Fifth Amendment grounds, citing violations of due process. And he said he believes that CNN and Acosta are likely to prevail in the case overall. He emphasized the "very limited" nature of the ruling and did not make a judgment on the First Amendment claims in the lawsuit.
Boutrous said the result was a "very good day for our Constitution as a general matter and for my clients in particular."
Boutrous and another veteran litigator, Ted Olson, both of the firm Gibson, Dunn & Crutcher, were retained by CNN in preparation for the lawsuit.
In an interview for Sunday's "Reliable Sources," Boutrous said he was "very happy to get the call" because he was following the Acosta dust-up and saying "this is wrong, this is outrageous."
He felt that this case was about much more than Acosta and CNN: "This was the threat to press credentials for all the reporters."
As for Friday's finding in CNN's favor, Boutrous said it showed the American system of checks and balances in action.
"We had cases both on the First and Fifth amendment issues, but also on the other questions that the court had to address: Was there irreparable harm? Does the balance of fairness favor Jim Acosta or the government and what's in the public interest? And the court, in a very clear straightforward way, walked through those legal principles and applied them. That's what we want our courts to do," Boutrous said. "That's part of our separation of powers process, where the courts are there to review what the other branches of government do. So the system worked exactly the way it's supposed to work."
"And, you know, we're not done," he added. "And we know that." But for now Acosta is back at work. He reported live from his usual position on the North Lawn of the White House on CNN's "The Situation Room" Friday evening.
Lawyers for both sides are expected to be back in court next week to discuss the timeline for further proceedings. The next phase, he said, is to obtain a preliminary injunction, which would last longer than a temporary restraining order.
"So unless we come to some agreement, or we agree to extend that, we go back into court and argue for a preliminary injunction which can be indefinite, much longer," Boutrous said.