The judge’s order comes at a time when the coronavirus is spreading quickly in American prisons, leading authorities across the country to release thousands of inmates to save lives and preserve medical resources. The decision of how soon Mr. Stone will be ordered to report to prison is up to the federal court’s probation and pretrial services office.

Mr. Trump has loomed large in the proceedings against Mr. Stone. He repeatedly complained on Twitter and to the news media that the judge, the jury and the prosecutors were being unfair to his friend.

The judge twice rebuked Mr. Trump in court, though not always by name. During Mr. Stone’s sentencing hearing, she simply described comments by a longtime friend of his as “entirely inappropriate.” She added pointedly, “There was nothing, phony, or disgraceful about the investigation or the prosecution.”

During a hearing on the defense’s request for a new trial, she said that the “the president himself has shone a spotlight on the jury” and read aloud one of his tweets attacking the jury forewoman as an example.

She also noted that Tucker Carlson, the Fox News commentator who is close to Mr. Trump, had also tried to stoke public anger about the case and the jurors. Attacking jurors “is completely antithetical to our entire system of justice,” she said, and could provoke someone “to take it out on them personally.”

Prosecutors argued that the defense motion for a new trial was “nothing more than an attempt to fuel its public campaign to undermine the jury’s verdict through a frivolous juror misconduct claim.” Nonetheless, in an unusual move, Judge Jackson held a four-hour hearing on the motion, summoning a dozen jurors back to the courtroom in February, three months after they had rendered a verdict.

Nancy Gertner, a retired federal judge who now teaches at Harvard Law School, said she believed the judge was being especially careful because the case had been so high-profile, not because the president was “breathing down her neck.”