An audio recording that includes new details from a 2021 meeting at which President Trump, then out of office, discusses holding secret documents he did not declassify has been released.

The recording, from a July 2021 interview that Mr. Trump gave at his Bedminster, New Jersey, resort for persons working on the memoir of his former chief of staff, Mark Meadows, is a critical piece of evidence in special counsel Jack Smith’s indictment of Mr. Trump over the mishandling of classified information. The recording was first aired Monday on CNN’s “Anderson Cooper 360.”

The special counsel’s indictment alleges that those in attendance at the meeting with Mr. Trump — a writer, a publisher, and two of Mr. Trump’s staff members — were shown classified information about a Pentagon plan of attack on an unspecified foreign country.

“These are the papers,” Mr. Trump said in a moment that seems to indicate he was holding a secret Pentagon document with plans to attack Iran. “This was done by the military, given to me.”

Mr. Trump’s reference to something he says is “highly confidential” and his apparent showing of documents to other people at the meeting could undercut his later claims in a Fox News Channel interview that he didn’t have any documents with him.

“There was no document. That was a massive amount of papers, and everything else talking about Iran and other things,” Mr. Trump said on Fox. “And it may have been held up or may not, but that was not a document. I didn’t have a document, per se. There was nothing to declassify. These were newspaper stories, magazine stories and articles.”

The 45th president pleaded not guilty earlier this month to 37 counts related to the alleged mishandling of classified documents kept at his Mar-a-Lago resort in Palm Beach, Florida.

A Trump campaign spokesman said the audio recording “provides context proving, once again, that President Trump did nothing wrong at all.”