But the government has appealed that ruling, arguing that no reporter’s privilege exists in criminal trials. Mr. Parker on Friday invoked a 1972 Supreme Court case holding that there is no reporter’s privilege against being forced to testify before a grand jury. He said the case was “clear” that the same rule should apply in a trial.

But Judge Diaz pronounced the precedent “clear as mud.” Among other problems, the fifth vote in the majority for that case came from a justice who wrote his own concurring opinion that appeared to give a broader reading of press freedoms than the other four.

A lawyer for Mr. Risen, Joel Kurtzberg, told the panel that no federal appeals court has adopted an understanding of First Amendment press protections as limited as the prosecutors’ view, urging them “not to accept the government’s invitation to be the first.”

A diverse coalition of more than two dozen media organizations, including The Times and Fox News, has filed a friend-of-the-court brief arguing that a qualified reporter’s privilege — allowing judges to protect reporters from testifying under some circumstances — is crucial for the “dissemination of news and information to the public.”

There is a possibility that the appeals court will invoke a technicality to sidestep the need to directly address the novel First Amendment questions raised by the case — at least for now. Mr. Kurtzberg argued that the appeals court lacks jurisdiction to review Judge Brinkema’s order at this stage because the judge has said she will revisit the question of Mr. Risen’s testimony midway through the trial.

Both Judge Diaz and Judge Traxler asked questions about the jurisdictional matter. But Mr. Parker voiced doubt that Judge Brinkema will change her mind and argued that the appeals court should rule on the issue now. Prosecutors need to know whether they can invoke Mr. Risen’s testimony in opening statements, he said, and it would be too late for prosecutors to appeal again once a jury is seated.

A lawyer for Mr. Sterling told the court that his client took no position in the dispute between Mr. Risen and prosecutors.