FORT PIERCE, Fla. — Federal prosecutors struggled to present a compelling case Monday for new restrictions on Donald Trump that would bar him from publicly attacking law enforcement officials, even as an attorney working for special counsel Jack Smith argued that the former president’s claims are false, inflammatory, and invite violence against FBI agents.

U.S. District Judge Aileen M. Cannon did not immediately rule on the motion to add a new condition to Trump’s bail on his pending trial for allegedly mishandling classified documents. Her approach suggested a decision is unlikely to come before Thursday’s scheduled debate between Trump, the presumptive Republican presidential nominee, and President Biden, his Democratic rival.

The hearing, which lasted about an hour and a half, came in response to Smith’s request that Trump’s bail be modified to prevent statements that would cause an imminent danger to law enforcement agents who have worked on the documents case.

Smith made the request last month after Trump suggested on social media that FBI agents were authorized or hoping to use deadly force when they searched his Florida home for classified documents in 2022. In that message, Trump posted that Biden’s Justice Department had “AUTHORIZED THE FBI TO USE DEADLY (LETHAL) FORCE. NOW WE KNOW FOR SURE, THAT JOE BIDEN IS A SERIOUS THREAT TO DEMOCRACY.’ The message also called Biden mentally unfit.

Trump’s accusation — one echoed and amplified by many of his supporters — was based on a standard description of the limits on the use of force by federal agents involved in the Mar-a-Lago search. That same legal language has been used for countless other FBI operations, including a voluntary search of Biden’s home in a different classified documents investigation.

Trump is already subject to gag orders in two of his other criminal cases, and while Smith’s latest request is not technically seeking a gag order, it would function in similar ways. The main difference is that any potential violations of his bail conditions could more quickly subject him to jail time.

Prosecutor David Harbach argued that Trump’s statements about FBI agents involved in the classified documents case “are dangerous” to the investigators who may testify against the former president, who faces 40 counts of willfully retaining classified information after leaving the White House and obstructing government efforts to retrieve them.

Harbach’s presentation was an uneven one, and the judge reacted sternly to his complaint at one point that he wasn’t being allowed to fully describe his reasoning.

“Mr. Harbach, I don’t appreciate your tone,” Cannon said, adding that she expected decorum “at all times. If you are unable to do that, I’m sure one of your colleagues can.’ Harbach later apologized to the judge.

Whatever line may exist between a person’s free speech rights and a criminal defendant’s restrictions on talking about his case, Harbach argued, Trump’s statements “are nowhere close to the line.”

The prosecutor called Trump’s social media following “a peculiarly potent tool’ that he brags about, well aware of how his followers will respond. “He knows it, he knows it,” Harbach insisted, waving his hand for emphasis. “Saying something like this is beyond irresponsible — it is dangerous.”

Cannon repeatedly suggested that a new restriction was unnecessary when she had already agreed to redact the names of FBI agents from public court filings. Harbach responded that some names were public on the internet and that Cannon shouldn’t wait for something terrible to happen before she enacts the restrictions.

Trump lawyer Todd Blanche argued that while the prosecutor kept insisting it was obvious Trump’s comments were dangerous, in reality the line the special counsel sought to draw was not clear to anyone outside the special counsel’s office. He said it was unfair to blame the presidential candidate for the actions of a handful of people who may be disturbed.

“Of course President Trump has absolutely no desire for anything bad to happen to law enforcement,” Blanche said. “It is a critique of President Biden and his Justice Department and it is completely fair and protected political speech.”

Cannon said she would give the parties until Wednesday to file additional evidence to support their arguments on the case docket. The hearing came after a morning session in which Trump’s lawyers argued Attorney General Merrick Garland had misused the Justice Department’s special counsel regulation to pursue Trump.

Similar arguments from other defendants who have been charged by special counsels have not succeeded.

Cannon showed a particular interest in how much special counsel appointments cost the government, at one point calling it a “significant” amount of money, even though the totals represent a drop in the bucket of Justice Department spending.

The most expensive special counsel investigation in recent years, conducted by Robert S. Mueller IIIand focused on alleged Russian interference in the 2016 election, cost about $32 million over several years. The Justice Department’s annual budget is more than $35 billion — meaning that Mueller’s work cost significantly less than 0.1 percent of the agency’s spending.

Trump lawyer Emil Bove argued that the Justice Department had fundamentally erred by running a stand-alone special counsel investigation without sufficient oversight.

“Our position is that more oversight from the Congress is required … for the extraordinary things going on” like the gag order request, Bove said. “Who authorized that? Was it the attorney general?”

In a hearing Friday on the constitutionality of the special counsel appointment, Bove argued that Smith had too much independence and said his appointment should have been approved by the Senate.

Cannon has shown an eagerness to delve into a host of legal issues raised by the defense, including some that are more commonly raised on appealin other cases. Before becoming a judge, Cannon was a prosecutor who worked on appellate issues, and long stretches of Monday morning’s hearing sounded more like an argument before an appeals court than a trial court.

In response, the government’s arguments were made Monday morning by James Pearce, a lawyer from the special counsel’s office with expertise in appellate issues.

Pearce said the defense claims that Smith’s office was not properly funded by the government were specious and lacking in any support in case law. Even if the judge found some flaw in the process, he said,there would be no meaningful remedy, because the Justice Department could easily draw the necessary funds from a different pool of agency money.

At one point, Cannon cautioned Pearce not to interrupt her while she was speaking, but the overall tenor of the morning hearing was polite, if somewhat tedious. Cannon did not immediately rule on the defense argument for dismissal of the indictment.