Lawyers for former President Donald J. Trump asked a federal judge on Monday night to indefinitely postpone his trial on charges of illegally retaining classified documents after he left office, saying that the proceeding should not begin until all “substantive motions” in the case had been presented and decided.

The written filing — submitted 30 minutes before its deadline of midnight on Tuesday — presents a significant early test for Judge Aileen M. Cannon, the Trump-appointed jurist who is overseeing the case. If granted, it could have the effect of pushing Mr. Trump’s trial into the final stages of the presidential campaign in which he is now the Republican front-runner or even past the 2024 election.

While timing is important in any criminal matter, it could be hugely consequential in Mr. Trump’s case, in which he stands accused of illegally holding on to 31 classified documents after leaving the White House and obstructing the government’s repeated efforts to reclaim them.

There could be complications of a sort never before presented to a court if Mr. Trump is a candidate in the last legs of a presidential campaign and a federal criminal defendant on trial at the same time. If the trial is pushed back until after the election and Mr. Trump wins, he could try to pardon himself after taking office or have his attorney general dismiss the matter entirely.

Some of Mr. Trump’s advisers have been blunt in private conversations that the former president is looking to winning the election as a solution to his legal problems. And the request for an open-ended delay to the trial of Mr. Trump and his co-defendant, Walt Nauta, one of his personal aides, presents a high stakes question for Judge Cannon, who came into the case already under scrutiny for having made decisions favorable to the former president in the early phases of the investigation.

Mr. Trump’s lawyers pitched their request to Judge Cannon as a plea for cautious deliberation and as a means of safeguarding democracy itself.

“This extraordinary case presents a serious challenge to both the fact and perception of our American democracy,” they wrote.

“The court now presides over a prosecution advanced by the administration of a sitting president against his chief political rival, himself a leading candidate for the presidency of the United States,” they wrote. “Therefore, a measured consideration and timeline that allows for a careful and complete review of the procedures that led to this indictment and the unprecedented legal issues presented herein best serves the interests of the defendants and the public.”

The lawyers also took note of the case’s unusual intertwining of law and politics, suggesting that Mr. Trump’s status as a candidate should be factored into the timing of the trial.

“President Trump is running for president of the United States and is currently the likely Republican Party nominee,” they wrote. “This undertaking requires a tremendous amount of time and energy, and that effort will continue until the election on Nov. 5, 2024.”

“Mr. Nauta’s job requires him to accompany President Trump during most campaign trips around the country,” they continued. “This schedule makes trial preparation with both of the defendants challenging. Such preparation requires significant planning and time.”

Mr. Trump’s filing came in response to one submitted last month by prosecutors working for the special counsel Jack Smith, who requested a trial date of Dec. 11. Judge Cannon, appearing to adopt the brisk calendar mandated by the Speedy Trial Act, had initially scheduled the case to go to trial in August.

On Monday, just hours before Mr. Trump’s lawyers requested a delay of the trial, a lawyer for Mr. Nauta asked Judge Cannon to delay a hearing to discuss the issue of the classified materials in the case that was scheduled for Friday. The defense and the prosecution ultimately agreed to delay the hearing, which will take place in Federal District Court in Fort Pierce, Fla. until next Tuesday.

The filing by Mr. Trump’s legal team presents Judge Aileen Cannon, a Trump appointee, with a key early decision about the pace of the proceeding.Credit…Southern District of Florida

Judge Cannon still has to grant her approval to that schedule change.

In making their case to delay the trial, Mr. Trump’s lawyers cited the expansive discovery evidence provided to them by the government.

The first discovery disclosure, they said, contained more than 833,450 pages of material, including about 122,650 emails and 305,670 other documents. The lawyers said that after subsequent troves of evidence were handed over, they would likely make more requests to the government for further information.

The lawyers also pointed to the complex process of deciding how to handle the sensitive materials at the heart of the case under the Classified Information Procedures Act — the subject of the hearing that had been scheduled for Friday. The lawyers strongly hinted that they were going to fight the government during the pretrial litigation over classified material, a process that could eat up significant amounts of time.

“In general, the defendants believe there should simply be no ‘secret’ evidence, nor any facts concealed from public view relative to the prosecution of a leading presidential candidate by his political opponent,” the lawyers wrote. “Our democracy demands no less than full transparency.”

Aside from its request for a delay, the filing served as a preview of Mr. Trump’s legal strategy as the lawyers laid out ways in which they planned to attack his indictment.

The lawyers suggested, for example, that they intended to challenge some of the charges he is facing by arguing that the Presidential Records Act permitted Mr. Trump to take documents with him from the White House. That interpretation of the Watergate-era law is odds with how legal experts interpret it and was not successful during an extended legal battle last year over an outside arbiter who was put in place to review a trove of materials seized by the F.B.I. from Mar-a-Lago, Mr. Trump’s private club and residence in Florida.

Mr. Trump’s lawyers also suggested that they might raise “constitutional and statutory challenges” to Mr. Smith’s authority as special counsel. Moreover, they laid the seeds for questioning whether an impartial jury could be seated at the trial while Mr. Trump was running for office.

“There is simply no question any trial of this action during the pendency of a presidential election will impact both the outcome of that election and, importantly, the ability of the defendants to obtain a fair trial,” they wrote.