“D.O.J. had full access to the president’s home, including personally handwritten notes, files, papers, binders, memorabilia, to-do lists, schedules, and reminders going back decades,” he added, referring to the Justice Department.

Mr. Bauer did not make clear in his statement where in the Wilmington home the documents had been found. The previous classified documents were found in the home’s garage and in a nearby storage space.

Another statement, from Richard Sauber, a member of the White House Counsel’s Office, said that the search had been conducted and finished at the home on Friday, and neither the president nor Jill Biden, the first lady, was at the residence at the time.

On Friday evening, even as investigators were still going through his home, Mr. Biden traveled to Rehoboth Beach, where he owns another house, to spend the weekend there. The president’s lawyers have said they searched the Rehoboth Beach home earlier this month and found no relevant documents. Officials have not said whether Justice Department investigators plan to conduct another search of the property.

In his statement on Saturday, Mr. Bauer said that the president’s cooperation with investigators was evidence that Mr. Biden and the White House were acting in good faith.

“We have attempted to balance the importance of public transparency where appropriate with the established norms and limitations necessary to protect the investigation’s integrity,” he wrote. “We will continue to do so throughout the course of our cooperation with D.O.J.”

News of the lengthy search, and the discovery of more classified materials, is certain to provide new ammunition to the president’s critics, including Republican members of the House, who have already demanded information about the documents and their potential impact on national security.