Magistrate Judge Deborah Robinson scheduled a status hearing for Friday afternoon in the case.
The other judge, Jackson, will conduct that hearing. A prosecutor in Mueller's office said the case will be prosecuted by the special counsel's team and the U.S. Attorney's Office for the District of Columbia.
Robinson allowed Stone to remain free on a $250,000 signature bond that was set at his first court appearance on Friday in Fort Lauderdale, Florida.
The judge stressed that Stone should have no contact with witnesses in the case. She also continued an order restricting his travel to between Florida and his future court appearances in Washington and to the New York City area.
In a barely audible voice, Stone said, "Yes, your honor," when Robinson reminded him of his release conditions.
During the hearing, a crowd outside of the E. Barrett Prettyman Courthouse held signs with messages that included, "Free Stone Fire Mueller," "We Stand with Stone," "Lock him Up," and "Dirty Traitor."
One person waved a Russian flag, and another played the Russian national anthem.
Mueller accuses Stone of lying to Congress about his alleged efforts to have WikiLeaks disseminate Democratic National Committee communications that were hacked hacked by Russian agents.
The indictment alleges Stone was was in contact with top-ranking Trump campaign officials about efforts to leak damaging information about the Democratic nominee Clinton right before Election Day.
It also says a senior official in the Trump campaign "was directed" to talk with Stone about potential future releases by WikiLeaks.
After his arraignment, Stone was interviewed by Alex Jones on Jones' InfoWars show, where he blasted the case against him. Jones routinely trafficks in unfounded conspiracy theories.
The outspoken Stone noted that there was not, despite some peoples' speculation that there would be, a gag order slapped on him at his arraignment.
"There was no suggestion of a gag order, but this would not have been the appropriate time, that, I suspect it would be coming from Judge Amy Berman Jackson, who essentially ordered torture for Paul Manafort, to torture him, and has rejected every challenge to Robert Mueller's authority," Stone said.
" She at this point will be the judge in my case, we'll see about that."
Jackson had revoked Manafort's $10 million release bond last June after he was charged with trying to tamper with witnesses while under house arrest awaiting two federal criminal trials related to crimes connected to his consulting work for pro-Russia politicians in Ukraine. After he was convicted of some charges at his first trial, Manafort pleaded guilty to other charges on the eve of his second scheduled trial.
"This is a lynching," Stone said. "This is a legal lynching of me because I appear on InfoWars, because I'm friends with Alex Jones, because I support Donald Trump and I supported him for president and I still support him, because I helped take down the evil queen, the foul-mouthed, short tempered, self-centered kleptocrat Hillary Clinton."
Stone echoed Jones when Jones called Clinton a "war criminal."
"And the irony of course is that I'm charged with perjury, lying before Congress, which I'm not guilty of," Stone said.
"They know that they have to take me down in order to take Donald Trump down, cause they know that they have to take InfoWars down because they don't want us to tell the American people what they're up to," Stone said. "It's insidious, it's ruthless- Alex, I'm facing potentially 45 years in jail."
WATCH: Trump associate Roger Stone arrested for allegedly lying in Mueller investigation