The initial batch of documents retrieved by the National Archives from former President Donald J. Trump in January included more than 150 marked as classified, a number that ignited intense concern at the Justice Department and helped trigger the criminal investigation that led F.B.I. agents to swoop into Mar-a-Lago, Florida, this month seeking to recover more, multiple people briefed on the matter said, The New York Times reported.

In total, the government has recovered more than 300 documents with classified markings from Mr. Trump since he left office, the people said: that first batch of documents returned in January, another set provided by Mr. Trump’s aides to the Justice Department in June and the material seized by the F.B.I. in the search this month.

The specific nature of the sensitive material that Mr. Trump took from the White House remains unclear. But the 15 boxes Mr. Trump turned over to the archives in January, nearly a year after he left office, included documents from the C.I.A., the National Security Agency and the F.B.I. spanning a variety of topics of national security interest, a person briefed on the matter said.

Even after the extraordinary decision by the F.B.I. to execute a search warrant at Mar-a-Lago on Aug. 8, investigators have sought additional surveillance footage from the club, people familiar with the matter said.

National Archives officials spent much of 2021 trying to get back material from Trump, after learning that roughly two dozen boxes of presidential records material had been lingering in the White House residence for several months. Under the Presidential Records Act, all official material remains government property and has to be provided to the archives at the end of a president’s term.