A federal magistrate judge unsealed on Wednesday additional portions of the affidavit that the F.B.I. used last summer to obtain a warrant to search for sensitive documents at Mar-a-Lago, former President Donald J. Trump’s private club and residence in Florida, revealing a few new details about how that extraordinary process had unfolded.

The newly unredacted sections of the affidavit suggested that prosecutors had based their search, in part, on surveillance footage from cameras near a storage room in the basement of Mar-a-Lago showing Walt Nauta, a personal aide to Mr. Trump, moving dozens of boxes in and out of the room days before federal prosecutors arrived to collect any sensitive records still in Mr. Trump’s possession.

Much of the material in the affidavit unsealed on Wednesday had already been made public in the expansive indictment of Mr. Trump and Mr. Nauta issued in Miami last month. That indictment charged the former president with 31 counts of illegally retaining national defense information and a separate count of conspiring with Mr. Nauta to obstruct the government’s efforts to reclaim them.

The judge who ordered the unsealing, Bruce E. Reinhart, had issued two previous orders unsealing separate portions of the warrant affidavit in response to media requests.

The newly revealed information included a photograph of dozens of boxes in the Mar-a-Lago storage room, as well as a detailed description of the various angles caught by the security cameras outside the room.

“The door to the storage room was painted gold and had no other markings on it,” the F.B.I. agent who drafted the affidavit wrote. “The door to the storage room is located approximately midway up the wall and is reachable by several wooden stairs.”

Echoing the indictment, the unredacted affidavit also noted that between May 24 and June 1, 2022, Mr. Nauta took 64 boxes out of the storage room at Mar-a-Lago but put back only 25 or 30 of them.

“The current location of the boxes removed from the storage room but not returned to it is unknown,” the affidavit said.

The newly released version of the affidavit did not, however, disclose all the reasons that federal prosecutors believed sensitive records remained at Mar-a-Lago even after two previous attempts to retrieve them from Mr. Trump.

In January 2022, Mr. Trump sent 15 boxes of government records from Mar-a-Lago to the National Archives, which discovered they contained nearly 200 classified documents. That prompted federal prosecutors to issue a subpoena in May for any additional materials bearing classified markings still in Mr. Trump’s possession. In June 2022, after conducting what was meant to be a diligent search of Mar-a-Lago, one of the former president’s lawyers, M. Evan Corcoran, gave the government another batch of 38 classified documents.

But even after those two initial groups of documents were returned, prosecutors suspected that Mr. Trump still had even more classified materials in his residence at Mar-a-Lago and in an adjacent area. The surveillance footage of Mr. Nauta was apparently only one piece of evidence underpinning that belief. A long section of the affidavit that follows the assertion by prosecutors that Mr. Trump had not returned everything he should have remains under seal.

It was Judge Reinhart who issued the Mar-a-Lago search warrant last August, resulting in federal agents hauling away more than 100 documents bearing classification markings.

Judge Reinhart has also been assigned as the magistrate judge to the prosecution of Mr. Trump and Mr. Nauta. Mr. Nauta is scheduled to be arraigned in Federal District Court in Miami on Thursday.

Among the new details revealed on Wednesday was that neither Mr. Corcoran nor another lawyer for Mr. Trump had told prosecutors that the former president had declassified any of the 38 classified documents handed over last June. That omission seemed to contradict an earlier statement the lawyers had made to the government, claiming that as president, Mr. Trump had “absolute authority” to declassify any material he wanted.

The newly unredacted portions of the affidavit also say that Mr. Corcoran told the government that he had been informed that there were no classified records “in any private office space or other location in Mar-a-Lago” — an assertion that the search of the property revealed to be untrue.

In March, a federal judge in Washington compelled Mr. Corcoran to provide records and to testify to a grand jury investigating the case, working around the usual protections of attorney-client privilege because she believed that Mr. Trump had misled Mr. Corcoran about where sensitive records were kept at Mar-a-Lago.