Shortly after learning that former President Donald J. Trump had been recorded discussing what appeared to be classified material describing military options for confronting Iran, federal prosecutors issued a subpoena to his lawyers seeking the return of all records that resembled the document he mentioned, two people familiar with the matter said on Friday.

But Mr. Trump’s legal team has informed the Justice Department that it was unable to find any such records in his possession, the people said. It is unclear whether prosecutors have been able to track down the document themselves, leaving open the possibility that the material remains at large or that the famously blustery Mr. Trump incorrectly described it on the recording.

The subpoena, which was issued in March, sought any and all records pertaining to Gen. Mark A. Milley, chairman of the Joint Chiefs of Staff, and to Iran, including maps or invasion plans, according to the people familiar with the matter. As part of their investigation, prosecutors have been asking witnesses whether Mr. Trump showed people a map he took with him when he left office that contains sensitive intelligence information.

The subpoena, which was reported earlier by CNN, mentioned General Milley because Mr. Trump brought up the classified document at a meeting as a way to rebut what he perceived as criticism from Mr. Milley about military decisions concerning Iran. The meeting, which took place in July 2021 at Mr. Trump’s golf club in Bedminster, N.J., was between Mr. Trump and two people helping with a book being written by the final Trump White House chief of staff, Mark Meadows.

A small number of aides to Mr. Trump also attended, including Margo Martin, who routinely sat in on and recorded book interviews granted by Mr. Trump, and Liz Harrington, the former president’s spokeswoman.

The subpoena appears to have been prompted by testimony that Ms. Martin gave about the recording to a federal grand jury investigating the documents case, according to the people familiar with the matter. A similar subpoena for records related to the document on Iran was issued to at least one other person who was at the meeting at Bedminster.

Steven Cheung, a spokesman for Mr. Trump, denounced what he said were conclusions based on “fake leaks that were clearly partisan.”

Throughout the investigation of Mr. Trump by the Justice Department and then by a special counsel, Jack Smith, prosecutors have expressed concern that Mr. Trump has failed to fully comply with efforts to retrieve all the classified material in his possession.

A central part of their inquiry is whether the former president obstructed the government’s repeated attempts to get the material back — first through a subpoena that was issued last May and then through a search warrant executed in August at Mar-a-Lago, Mr. Trump’s private club and residence in Florida.

After the F.B.I. descended on Mar-a-Lago and discovered about 100 classified documents that were there in violation of the subpoena, Mr. Trump’s lawyers conducted their own search of the compound and of other properties connected to Mr. Trump. During those searches at the end of last year, the lawyers discovered at least two more documents bearing classification markings.

Before all of these searches were conducted, Mr. Trump handed over two separate batches of classified material to the government. One batch was given to the National Archives in January 2022. The other was given to a federal prosecutors who visited Mar-a-Lago in June 2022, seeking to collect everything they could in response to the subpoena they had issued the month before.

In the batch that went to the archives, there was one document concerning military options for Iran, according to one of the people familiar with the matter. But it remained unclear whether that document was the same one that Mr. Trump had mentioned in the recording.

Even if the government is never able to find the document Mr. Trump discussed, his statements on the recording could prove damaging to him as Mr. Smith’s team moves toward concluding its investigation and turns to the question of whether to file charges.

On the recording, Mr. Trump signaled his awareness of his inability to declassify the document because he had already left office, according to people familiar with the tape.

If that description proves correct, it would undercut one of the key defenses that Mr. Trump’s advisers have offered in their effort to justify why he was allowed to hold onto some of the government’s most sensitive secrets after leaving the White House. They have argued that Mr. Trump, while still in office, had declassified all the material he took with him when he left.