In recent weeks, Mr. Smith’s office has drilled down on the question of whether Mr. Trump and some of his aides sought to interfere with the government’s efforts to obtain security camera footage from Mar-a-Lago that could shed light on how documents were stored at the property and who had access to them.

Prosecutors have also been studying recorded audio notes made by a lawyer for Mr. Trump, M. Evan Corcoran. The notes pertain to a period last year when Mr. Corcoran was representing Mr. Trump after a subpoena from the Justice Department seeking the return of all classified materials in the former president’s possession.

The notes also encompassed a search that Mr. Corcoran undertook last June in response to the subpoena for any relevant records being kept at Mar-a-Lago. Mr. Corcoran was forced to turn over the notes after prosecutors convinced a federal judge that they had sufficient evidence of a crime to pierce attorney-client privilege, which typically would shield such material from scrutiny.

In a one-page letter from Mr. Trump’s lawyers to Mr. Garland, which Mr. Trump posted on his Truth Social account on May 23, the lawyers did not cite any specific complaints by his legal team, but instead broadly asserted that Mr. Trump had been treated unfairly by the Justice Department through the investigations led by Mr. Smith. Along with the classified documents case, prosecutors under Mr. Smith are also scrutinizing efforts by Mr. Trump and his aides to overturn the results of the 2020 election.

The letter to Mr. Garland was an abbreviated version of a longer one that contained a more detailed account of the concerns by Mr. Trump’s lawyers, according to two people familiar with the matter. Those included the ways in which grand juries have been used in the special counsel’s investigations and attempts to strong-arm defense lawyers involved in the cases, the people said.

Mr. Trusty, who worked at the Justice Department for more than two decades, knows Mr. Smith well: The two worked with each other a decade ago, when Mr. Trusty was a high-ranking prosecutor in the department’s criminal division and Mr. Smith was the head of the public integrity unit.

The Trump legal team’s visit to the Justice Department, first reported by CBS News, came as signs have emerged that Mr. Smith could soon make a decision about whether to seek charges in the documents case. The status of his other line of inquiry, into Mr. Trump’s efforts to reverse his election loss and how they contributed to the assault on the Capitol by his supporters on Jan. 6, 2021, remains less clear.