"This is a criminal proceeding and not a public relations campaign," the judge said, She admonished Stone for treating the run-up to the trial "like a book tour."
Jackson said that any potential gag order would bar prosecutors, Stone and his lawyers from discussing the case publicly. But she noted it wouldn't prevent them from talking about "immigration, foreign relations or Tom Brady," the quarterback of the New England Patriots.
The judge, who has not made up her mind about a gag order, asked prosecutors and Stone's defense lawyers to submit briefs on a possible gag order by Feb. 8.
Stone addressed Jackson only to say that he understood that he was not allowed to talk to potential witnesses in the case.
Prosecutors in Mueller's office told Jackson on Friday that they are looking at an October date for Stone's trial. But the judge said she is more inclined to schedule the trial for July or August, though she added that a fall date would not be unreasonable.
Jackson has hit other Mueller targets with gag orders. In November 2017, Jackson ordered lawyers for Trump's former campaign chairman Paul Manafort to limit their comments to the press.
"I want to make it clear, from this point on, that I expect counsel to do their talking in this courtroom and in their pleadings, and not on the courthouse steps," Jackson said at that time.
Before Friday's hearing, Stone's lawyer, Grant Smith, told CNBC that he and his client have "no expectation that the judge is entertaining" a gag order.
"The government has never mentioned it, and if the judge on her own motion does that, Mr. Stone will vigorously defend his First Amendment rights," Smith said.
It's unclear what that defense might entail. David Weinstein, a defense attorney and former federal prosecutor, told CNBC that "Stone is barking up the wrong tree if he thinks, even with his experienced stable of First Amendment lawyers, that he can skirt around a gag order imposed by Judge Berman."
Stone, Republican political operative and self-described dirty trickster, has been anything but shy about talking to the press since his indictment by Mueller's attorneys.
He was arrested at his home in Fort Lauderdale, Florida, on Jan. 25, and was released on a $250,000 bond later that day by a federal judge in a Florida district court. Minutes later — while he was apparently still inside the courthouse — Stone had a phone interview with Alex Jones, head of right-wing conspiracy site Infowars.
After that call ended, Stone greeted a mix of supporters, critics and media figures outside, where he imitated former President Richard Nixon's "V sign" pose and told the crowd that there are "no circumstances whatsoever under which I will bear false witness against the president, nor will I make up lies to ease the pressure on myself."
On Tuesday, Stone pleaded not guilty to the seven counts against him. Afterward, he again appeared on Infowars, where he called the case a "lynching" orchestrated by Mueller "because I support Donald Trump," and because "I helped take down" Trump's 2016 opponent, Hillary Clinton.
After his arraignment, Stone, who prides himself on having a refined sartorial taste, participated in a video for conservative outlet The Daily Caller explaining how to dress for court.
