A top Justice Department official told former President Donald J. Trump’s lawyers in recent weeks that the department believed he had not returned all the documents he took when he left the White House, according to two people briefed on the matter.
The outreach from the official, Jay I. Bratt, who leads the department’s counterintelligence operations, is the most concrete indication yet that investigators remain skeptical that Mr. Trump has been fully cooperative in their efforts to recover documents the former president was supposed to have turned over to the National Archives at the end of his term.
It is not clear what steps the Justice Department might take to retrieve any material it thinks Mr. Trump still holds.
And it is not known whether the Justice Department has gathered new evidence that Mr. Trump has held onto government material even after the court-authorized search in August of his private club and residence in Florida, Mar-a-Lago, and 18 months of previous efforts by the federal government to convince the former president to return what he had taken on leaving office.
The Justice Department declined to comment.
The outreach from the department prompted a rift among Mr. Trump’s lawyers about how to respond, with one camp counseling a cooperative approach that would include bringing in an outside firm to conduct a further search for documents and another advising Mr. Trump to maintain a more combative posture.
The more combative camp, the people briefed on the matter said, won out.
The government has found more than 300 classified documents in material that had been kept at Mar-a-Lago, including some marked as containing the most sensitive information that would cross the president’s desk.
But the Justice Department has previously signaled doubts that Mr. Trump had turned over everything in his possession. Shortly after the search in August, it was revealed that federal investigators had found dozens of empty folders at Mar-a-Lago marked as containing classified information. The disclosure raised further questions about whether the Justice Department had indeed recovered all the classified materials that may have been taken out of the White House.
The empty folders were found during the search of Mar-a-Lago along with 40 other empty folders that said they contained sensitive documents that should be returned “to staff secretary/military aide,” according to a court filing. Agents found the empty folders along with seven documents marked as “top secret” in Mr. Trump’s office. Investigators also found 11 more marked as “top secret” in a storage room.
The department has also signaled in court filings that it has continued to try to determine whether more government materials remain unaccounted for. In a September court filing, the Justice Department complained that a judge’s decision to bar the authorities from having access to the documents they seized in the raid — later partially reversed by a federal appeals court — would limit their ability to determine whether documents were missing.
The injunction, the department said in the filing, “appears to bar the FBI and DOJ from further reviewing the records to discern any patterns in the types of records that were retained, which could lead to identification of other records still missing.”
More on the Trump Documents Inquiry
The department added that the injunction “would prohibit the government from using any aspect of the seized records’ contents to support the use of compulsory process to locate any additional records.”
Among the potential crimes that the department cited in seeking the search warrant for Mar-a-Lago was obstruction.
Justice Department officials and representatives of Mr. Trump have held a number of discussions in recent weeks. After the call from Mr. Bratt, who has led the Justice Department’s investigation into Mr. Trump’s handling of the documents, Mr. Trump initially agreed to go along with the advice of one of his lawyers, Christopher M. Kise, who suggested hiring a forensic firm to search for additional documents, according to the people briefed on the matter.
But other lawyers in Mr. Trump’s circle — who have argued for taking a more adversarial posture in dealing with the Justice Department — disagreed with Mr. Kise’s approach. They talked Mr. Trump out of the idea and have encouraged him to maintain an aggressive stance toward the authorities, according to a person familiar with the matter.
It is unclear at which property Mr. Kise wanted a voluntary search by an outside group to be conducted. Along with his Mar-a-Lago club in Palm Beach, Fla., Mr. Trump frequently spends time at his club in Bedminster, N.J., and an office in Manhattan.
The disagreement among the lawyers about how to respond to the Justice Department helped create a fissure within Mr. Trump’s legal team and led, in part, to the minimization of Mr. Kise’s role in Mr. Trump’s legal team in recent weeks.
Taylor Budowich, a spokesman for Mr. Trump, criticized the Justice Department.
“The weaponized Department of Justice and the politicized F.B.I. are spending millions and millions of American tax dollars to perpetuate witch hunt after witch hunt,” he said.
Mr. Trump’s apparent reluctance so far to cooperate puts the department in the fraught position of having to decide from among an array of difficult choices, including whether to give up on trying to obtain the documents, issuing a subpoena for them, obtaining another search warrant or pushing for Mr. Trump to attest under oath that he has handed over all the materials in his possession.
Bob Litt, a longtime national security lawyer, said the Justice Department has a number of options short of carrying out another search warrant. One would be to file a motion in the ongoing court fight over the documents, seeking either return of the documents or a statement under oath from Mr. Trump that he has returned all the documents. By doing so, Mr. Litt said, the department could back Mr. Trump into a corner.
How the department proceeds, he said, would likely be influenced by whether the department believes the documents in question are highly sensitive.
“They could say to the court that in lieu of seeking a search warrant we’re bringing this to the court,” Mr. Litt said. “The goal is to get Trump to go on the record because he has a history of saying things out of court that he won’t go on the record for.”
The lingering questions of missing documents appear to be part of a larger issue the Justice Department and National Archives are confronting with the Trump White House, which routinely flouted federal record-keeping laws.
Last week, the National Archives told a congressional committee that members of Mr. Trump’s administration had still not turned over all presidential records that exist outside of government coffers.
The agency said that there could be legal consequences for those individuals who fail to return the presidential records, including work-related messages from personal email accounts.
The acting U.S. archivist, Debra Steidel Wall, told the congressional committee that the agency would consult with the Justice Department on whether to “initiate an action for the recovery of records unlawfully removed.”
“While there is no easy way to establish absolute accountability, we do know that we do not have custody of everything we should,” Ms. Wall wrote to Representative Carolyn B. Maloney, Democrat of New York and the chairwoman of the Oversight Committee.
Ben Protess, Glenn Thrush and Matt Apuzzo contributed reporting.