The US Department of Justice has said it will accept one of Donald Trump’s suggestions for the neutral arbiter to review documents seized during the FBI’s raid of the former president’s Mar-a-Lago estate last month.

In a court filing late on Monday, lawyers for the department said that, in addition to the two retired judges whom they earlier recommended to fill the “special master” role, they would also be satisfied with one of the Trump team’s selections.

Raymond Dearie, the former chief judge of the federal court in the Eastern District of New York, is currently on senior active status, and the department said he had indicated he was available and “could perform the work expeditiously” if appointed.

The Trump team said earlier on Monday that it opposed both Justice Department selections.

Last week, US District Judge Aileen Cannon agreed with a request from Trump’s team to freeze the government’s review of the files until a special master is appointed to check the documents for any potential executive privilege or attorney-client privilege.

It is now up to Cannon to choose whether to name 78-year-old Dearie to the case.

The Justice Department’s accommodation could help accelerate the selection process and shorten any delays caused by the appointment of the special master.

The department is conducting an investigation into Trump’s possible mishandling of classified material in an unprecedented criminal probe targeting a former president.

The search warrant for Mar-a-Lago, Trump’s Florida home, said federal agents were investigating potential violations of three different federal laws, including one that governs gathering, transmitting or losing defence information under the Espionage Act.

An unsealed property receipt also showed the FBI seized 11 sets of classified documents, some of which were marked not only top secret but also “sensitive compartmented information”.

That term refers to a special category meant to protect the nation’s most important secrets that, if revealed publicly, could cause “exceptionally grave” damage to US interests.

Trump’s team has rejected the probe as “misguided”, and earlier this week argued in a court filing that US law grants presidents “extraordinary discretion” to label documents from their administration as presidential or personal.

His lawyers described the investigation as a “document storage dispute that has spiraled out of control” and accused the government of seeking to make it a crime for the former president to hold on to “his own Presidential and personal records”.

They also rejected the argument that US national security may have been harmed by Trump’s possession of the records, saying there is no indication that potentially secret files were exposed to anyone.

Trump’s legal team had urged Cannon to keep in place the directive that temporarily halted key aspects of the Justice Department’s criminal probe.

The Justice Department late last week appealed the judge’s order, asking Cannon – a Trump appointee – to partially suspend her own ruling and allow the review of classified documents to proceed pending appeal.

Department lawyers have rejected the idea that the documents belonged to Trump or that Mar-a-Lago was a permissible place to store them.

Meanwhile, a congressional committee said in a letter on Tuesday that the National Archives is still not certain that it has custody of all Trump’s presidential records even after the FBI search.

The House Committee on Oversight and Reform revealed that staff at the Archives on an August 24 call could not provide assurances that they have all of Trump’s presidential records. The committee in the letter asked the Archives to conduct an assessment of whether any Trump records remain unaccounted for and potentially in his possession.

“In light of revelations that Mr. Trump’s representatives misled investigators about his continued possession of government property and that material found at his club included dozens of ‘empty folders’ for classified material, I am deeply concerned that sensitive presidential records may remain out of the control and custody of the US Government,” Representative Carolyn Maloney, the chairwoman of the Oversight Committee, wrote in the letter.

The House committee has jurisdiction over the Presidential Records Act, a 1978 law that requires the preservation of White House documents as property of the US government.