A lawyer for former US President Donald Trump reportedly signed a false statement saying all classified material held in boxes at Trump's Mar-a-Lago residence had been returned to the government.

The letter signed by the lawyer in June raises fresh questions about whether or not Trump or his legal representatives lied to federal authorities in their ongoing investigation into the handling of classified materials from his time in the White House, the New York Times reported on Saturday.

As part of the probe, the FBI last week executed a search warrant at Mar-a-Lago, with agents removing 11 sets of classified documents.

The Times noted in its report that the lawyer's statement "is a possible indication that Mr Trump or his team were not fully forthcoming with federal investigators about the material".

The statement was signed by one of Trump's lawyers after Jay Bratt, a top national security official in the US Department of Justice (DOJ), visited Trump's South Florida beach club on June 3, according to the New York Times. Bratt met with two Trump lawyers to discuss the handling of classified information during the visit, the newspaper said, citing unnamed sources familiar with the matter.

The sources did not identify exactly when the letter was signed or by whom. It was part of an ongoing correspondence with the Justice Department over the issue.

It was previously reported that Justice officials left the June meeting at Mar-a-Lago with classified information, investigators developed evidence, including from a witness, that led them to believe there was more classified information in documents stored at the complex.

Mar-a-Lago in Palm Beach, Florida. Former President Donald Trump says the FBI is conducting a search of his estate. Photo / AP

The former president was indignant that the FBI had undertaken a surprise search of Mar-a-Lago and suggested that his team had been complying with the government's requests.

"[T]hey didn't need to "seize" anything," he said in a Truth Social post Friday. "They could have had it anytime they wanted without playing politics and breaking into Mar-a-Lago. It was in secured storage, with an additional lock put on as per their request... …They could have had it anytime they wanted—and that includes LONG ago. ALL THEY HAD TO DO WAS ASK."

Court documents unsealed and released on Friday identify three federal crimes that the DOJ is examining as part of its investigation: violations of the Espionage Act, obstruction of justice and criminal handling of government records. The inclusion of the crimes indicated the department had probable cause to investigate those offences as it was gathering evidence in the search. No one has been charged with a crime.

The June meeting included Trump's lawyers Evan Corcoran, Christina Bobb and federal investigators, including Jay Bratt, the chief of the counterintelligence and export control section at the Justice Department, CNN reports.

Trump spokesperson Taylor Budowich said in a statement: "Just like every Democrat-fabricated witch hunt previously, the water of this unprecedented and unnecessary raid is being carried by a media willing to run with suggestive leaks, anonymous sources, and no hard facts.

"The Biden administration thought they could 'get Trump', instead, they've been exposed as the very people who turn democracies into dictatorships."

The National Archives, charged with collecting and sorting presidential material, has previously said at least 15 boxes of White House records were recovered from Trump's Mar-a-Lago resort — including some that were classified.