This article is more than
1 year oldIn a filing late on Friday night, the prosecutors said they feared Mr Trump might disclose confidential evidence.
They justified the move citing a post by Mr Trump shared on Friday, saying it targeted people involved in the case.
But Mr Trump's team insisted the post was directed at political opponents.
On the Truth social network Mr Trump wrote "IF YOU GO AFTER ME, I'M COMING AFTER YOU!" on Friday afternoon, just a day after he pleaded not guilty to four charges in the alleged election fraud case.
The charges - which include conspiracy to defraud the US, tampering with a witness and conspiracy against the rights of citizens - stem from the former president's actions in the wake of the 2020 election, including around the 6 January Capitol riot.
In their filing, the office of Special Counsel Jack Smith said the post raised concerns that Mr Trump could publicly reveal secret material, including grand jury transcripts obtained from prosecutors.
Noting that Mr Trump has a history of attacking judges, attorneys and witnesses against him, Mr Smith's office warned that his behaviour could have "a harmful chilling effect on witnesses or adversely affect the fair administration of justice in this case".
The Republican has already hit out against the special counsel, telling a crowd of supporters in Alabama on Friday that Mr Smith was a "deranged human being" and "a bad guy".
The filing added that Friday's post "specifically or by implication" referred to those involved in the criminal case against him.
It added the order which they are seeking - known as a protective order - would not be "overly restrictive", saying that it did not prevent Mr Trump and his team discussing the case in the media and would allow him to access discovery materials for use in his defence.
"All the proposed order seeks to prevent is the improper dissemination or use of discovery materials, including to the public," the filing said.
Judge Tanya Chutkan gave Mr Trump's legal team until 17:00 local time on Monday to respond to the submission. Mr Trump's lawyers asked for three more days, but the judge denied their request.
In a statement shortly after the filing, a spokesperson for Mr Trump defended the social media post and insisted that he had been targeting political opponents.
"The Truth post cited is the definition of political speech," the statement said, adding that it was in response to "dishonest special interest groups" and political action committees attacking him.
Speaking later at a campaign rally in South Carolina, Mr Trump said he regards his indictment as a "great badge of honour".
He told the event that he was being indicted "because they're afraid of all of us", and wanted to silence him and his supporters - but America would be free again if he returned to the White House.
Judge Chutkan, a noted hardliner on cases against those accused of participation in the Capitol riots, is expected to call in attorneys from both sides on 28 August to discuss setting a trial date.
Prosecutors have already said that the case would benefit from a speedy trial.
But Mr Trump's defence attorney John Lauro has said his team will need more time to prepare. He said the prosecution's timeline was "somewhat absurd" given that the investigation itself had taken three years.
Mr Trump now faces five upcoming trials - three criminal trials which include the classified documents case, the hush money case, and these election charges; and two civil trials over business practices and alleged defamation of a woman who accused him of rape.
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