Special counsel Jack Smith said in a court filing Tuesday that former President Donald Trump has made "daily extrajudicial statements that threaten to prejudice the jury pool" in the 2020 election subversion case.

The allegation arose in a court fight that remains largely under seal, so additional details are not public. The brief reference to Trump's statements affecting the jury pool at the Washington, DC, courthouse came in a public filing in the federal criminal case.

Smith's office has been sparring with Trump's team over how much of the underlying sealed dispute should be made public.

Prosecutors tried earlier Tuesday to file court documents partially under seal -- and partially on the public docket.

But Trump's team argued that the filings should not be posted to the court's public docket until they have 14 days to respond -- the amount of time set out by default court rules.

Smith's team shot back in the public filing: "Such a requirement would grind litigation in this case to a halt, which is particularly infeasible given the pressing matters before the Court — including the defendant's daily extrajudicial statements that threaten to prejudice the jury pool in this case, as described in the Government's motion."

US District Judge Tanya Chutkan has ordered both sides to file additional legal briefs on whether and how the underlying Smith submission should be posted on the docket, with a Trump brief due on September 11 and a reply brief due from prosecutors on September 13.

Chutkan said that either party may file their brief under seal.