At least one lawyer for former President Donald J. Trump signed a written statement in June asserting that all material marked as classified and held in boxes in a storage area at Mr. Trump’s Mar-a-Lago residence and club had been returned to the government, four people with knowledge of the document said.

The written declaration was made after a visit on June 3 to Mar-a-Lago by Jay I. Bratt, the top counterintelligence official in the Justice Department’s national security division.

The existence of the signed declaration, which has not previously been reported, is a possible indication that Mr. Trump or his team were not fully forthcoming with federal investigators about the material. And it could help explain why a potential violation of a criminal statute related to obstruction was cited by the department as one basis for seeking the warrant used to carry out the daylong search of the former president’s home on Monday, an extraordinary step that generated political shock waves.