In a court filing on Friday, the Justice Department said its inability to get access to the non-classified documents held at Mr Trump's estate was interfering with its investigation into the retention of government records at the Florida property that pertain to the classified records.
The Justice Department is asking the 11th Circuit Court of Appeals to order all papers be filed in the case by November 11, and hold any necessary hearing in the case as soon as that briefing is completed.
Mr Trump's lawyers are opposing the request, the government said. They did not respond to a request for comment.
The Justice Department said an expedited schedule may allow the government, if it wins the appeal, “to more quickly resume its full investigation without restraints on its review and use of evidence seized pursuant to a lawful search warrant”.
The government lawyers added that, if the Atlanta-based appeals court rules in the Justice Department's favour, it would end the litigation over materials seized in the search as well as the outside review of those documents.
That review, being conducted by special master Senior US District Judge Raymond Dearie, is set to end by December 16.
The appeals court last month sided with the Justice Department in lifting parts of the ruling from US District Judge Aileen Cannon that had prevented the department from relying on classified materials taken in the search as part of its investigation, such as bringing up the sensitive records' contents in witness interviews or presenting charges to a grand jury.
The court also blocked Judge Dearie from accessing the classified records as part of his proceedings.
Judge Cannon on September 5 granted Mr Trump’s request for a third-party review of the seized documents, over the objections of the Justice Department. That process has already been delayed, as Mr Trump and the government have not yet been able to secure a contract with an outside vendor to host the documents as part of the review.
On Thursday, she also rejected Judge Dearie’s instruction that Mr Trump verify the list of documents taken from the property, after the former president's lawyers argued that requirement was outside the scope of the special master’s authority.
Mr Trump has claimed without evidence that FBI agents planted evidence as they searched his resort on August 8, but his lawyers have not repeated those allegations in court.