He also complained about the results of former special counsel Robert Mueller's investigation, which concluded last summer.
In a series of three tweets to his 72.6 million followers, the president quoted comments from Fox News legal contributor Andrew Napolitano -- who has publicly pressed Judge Amy Berman Jackson to accept Stone's request for a new trial.
"Judge Jackson now has a request for a new trial based on the unambiguous & self outed bias of the foreperson of the jury, whose [sic] also a lawyer, by the way. 'Madam foreperson, your [sic] a lawyer, you have a duty, an affirmative obligation, to reveal to us when we selected you the ... existence of these tweets in which you were so harshly negative about the President & the people who support him," Trump tweeted.
He added, "Don't you think we wanted to know that before we put you on this jury.' Pretty obvious he should (get a new trial). I think almost any judge in the Country...would order a new trial, I'm not so sure about Judge Jackson, I don't know." @Judgenap (Andrew Napolitano) @foxandfriends."
A DOJ official said Barr personally supported the department lawyers' motion that objected to Stone's team calling for a new trial.
Barr personally intervened in the case last week to overrule the line prosecutors who had recommended Stone be sentenced to seven to nine years in prison, just hours after Trump tweeted that the original recommendation was a "miscarriage of justice."
In an exclusive interview with ABC News last week, Barr said that the president's public comments about the department's work make his job "impossible."
"I think it's time to stop the tweeting about Department of Justice criminal cases," Barr told ABC News Chief Justice Correspondent Pierre Thomas. "I cannot do my job here at the department with a constant background commentary that undercuts me."
He also insisted in the interview that he made his decision to revise the sentencing request for Stone independent of the president's tweet.
A DOJ spokesperson declined to comment when asked by ABC News about the president's tweets Tuesday morning.
In a conference call with Stone, his defense team and two DOJ prosecutors on Tuesday, Jackson said that she has decided not to delay Stone's sentencing, which is set for Thursday, despite the defense's request it be postponed. The scheduling call was set after lawyers for Stone filed the sealed motion seeking a new trial due to alleged jury misconduct late last week.
In keeping Stone's sentencing date as planned, Jackson assured Stone and his attorneys, "I will ensure that the execution of sentence and the deadline for the filing of a notice of appeal will be deferred to ensure that the defendant has had the benefit of the ruling on the motion before filing any notice of appeal."
Details of both the request and the Justice Department's opposition are mostly unknown while under seal. Late Tuesday, Jackson set a deadline of Feb. 24 for the defense to respond to the government's opposition.
After the department rejected a sentencing recommendation for Stone, four prosecutors withdrew from the case last week, including two individuals who were veterans of special counsel Robert Mueller's investigation.
Trump seemed to falsely imply that all four prosecutors worked on the Mueller probe, which he characterized as a "fraudulent investigation," while threatening to sue "everyone all over the place."
In a final tweet Tuesday, the president said that he has not ruled out legal action.
"BUT MAYBE I STILL WILL," he tweeted. "WITCH HUNT!"
ABC News' Alexander Mallin, Jordyn Phelps and Ali Dukakis contributed to this report