Defense lawyers asked both the Justice Department and a federal judge on Monday night to stop the special counsel, Jack Smith, from publicly releasing a report detailing his investigation into President-elect Donald J. Trump’s mishandling of classified documents after he left office in 2021.

The two-pronged attempt to block the report’s release arrived as Mr. Trump was only two weeks away from being sworn in for a second term as president. With the case against Mr. Trump already dismissed, the report would essentially be Mr. Smith’s final chance to lay out damaging new details and evidence, if he has any.

Mr. Trump’s lawyers, in an aggressively worded letter to Attorney General Merrick B. Garland, said they had recently been shown a draft copy of Mr. Smith’s report, calling it an example of the special counsel’s “politically motivated attack” against Mr. Trump. They demanded that Mr. Garland not allow Mr. Smith to make the report public and “remove him promptly” from his post.

“The release of any confidential report prepared by this out-of-control private citizen unconstitutionally posing as a prosecutor would be nothing more than a lawless political stunt, designed to politically harm President Trump,” the lawyers wrote. In separate court papers, lawyers for Mr. Trump’s two co-defendants in the classified documents case, Walt Nauta and Carlos De Oliveira, sought a more direct path toward stopping the release of Mr. Smith’s report. They asked the judge who oversaw the case, Aileen M. Cannon, to issue an emergency order to bar Mr. Smith from making the report public until the case “has reached a final judgment and appellate proceedings are concluded.”

Both attempts to block Mr. Smith could face an uphill battle.

Mr. Trump’s lawyers have no power to force Mr. Garland to stop the report from coming out, and their letter amounted to little more than a belligerent request. It is also unclear whether Judge Cannon would have the authority to tell the attorney general how to handle a report by a special counsel that he himself appointed, especially when the case is technically out of her hands and in front of an appeals court.

That happened because Judge Cannon threw out the case in its entirety in July, ruling, in the face of decades of precedent, that Mr. Smith had been unlawfully appointed as special counsel. Mr. Smith and his deputies challenged that decision, and it was being considered by a federal appeals court in Atlanta when Mr. Trump won the election in November.

Citing Justice Department policy against prosecuting a sitting president, Mr. Smith dropped the appeal where Mr. Trump was concerned, effectively ending his role in the case. But he did not drop the appeal against Mr. Nauta and Mr. De Oliveira, and federal prosecutors in Florida now plan to pursue it when Mr. Smith steps down, likely before Inauguration Day on Jan. 20.

Mr. Smith has also moved to dismiss the other federal case he brought against Mr. Trump, accusing him of plotting to overturn the 2020 election. It remains unclear when Mr. Smith plans to file a report in that case and whether it will accompany the report on the documents prosecution or be contained in a separate document.

The effort by Mr. Trump’s lawyers to block the release of the report was only their latest attempt to kill or push back any legal filings or proceedings that might be embarrassing or damaging to the president-elect.

Earlier on Monday, a state judge in Manhattan rejected Mr. Trump’s most recent attempt to delay his sentencing on 34 felony charges, saying that the hearing would go on as scheduled on Friday.

Justice Department regulations call for all special counsels to file reports to the attorney general explaining why they filed the charges they did, and why they decided not to file any other charges they might have been considering. The attorney general can then decide whether to release the report to the public.

It remains unclear when Mr. Smith was planning to finish his report in the classified documents case. But the lawyers for Mr. Nauta and Mr. De Oliveira said in their court papers that the report was likely to be released “within the next few days.”

Should either or both reports eventually see the light of day, it is possible they will not contain much in the way of new or revelatory information.

The report in the classified documents case could be complicated by the fact that it would likely have to undergo a careful review by the intelligence community for any classified information it contained. The report in the election interference case might not break significant new ground, if only because in October Mr. Smith filed a sprawling, 165-page brief laying out the evidence he planned to offer at trial.

Still, in their letter to Mr. Garland, Mr. Trump’s lawyers complained that the draft report in the classified documents case said that Mr. Trump had “harbored a ‘criminal design’” and was the “head of the criminal conspiracies” detailed in the indictment. The draft also said, the lawyers wrote, that “Mr. Trump violated multiple federal criminal laws.”

Mr. Trump’s lawyers turned the tables on Mr. Smith, accusing him of “unethical” conduct and “improper activities.” Those accusations had possible implications for future retribution against Mr. Smith, given that two of the lawyers who signed the letter to Mr. Garland, Todd Blanche and Emil Bove, have been chosen by Mr. Trump to serve in high positions in his Justice Department.While Mr. Garland has not said publicly whether he intends to release either report by Mr. Smith, he has done so in the past with other reports by other special counsels.

In February, for example, Mr. Garland permitted the release of a report by the special counsel Robert K. Hur concerning President Biden’s handling of classified materials after he served as vice president. The report concluded that criminal charges were not warranted, but also offered an unflattering assessment of Mr. Biden’s memory and cognitive capacity in the middle of the 2024 presidential campaign.